Binary-safe file read (original) (raw)

fread

(PHP 4, PHP 5, PHP 7)

fread — Binary-safe file read

Description

fread ( resource $handle , int $length ) : string

Parameters

handle

A file system pointer resourcethat is typically created using fopen().

length

Up to length number of bytes read.

Return Values

Returns the read string or FALSE on failure.

Examples

Example #1 A simple fread() example

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mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>p</mi><mi>e</mi><mi>n</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mi>f</mi><mi>i</mi><mi>l</mi><mi>e</mi><mi>n</mi><mi>a</mi><mi>m</mi><mi>e</mi><mo separator="true">,</mo><mi mathvariant="normal">&quot;</mi><mi>r</mi><mi mathvariant="normal">&quot;</mi><mo stretchy="false">)</mo><mo separator="true">;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>k</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>k</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><mo>−</mo><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>m</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>x</mi><mi>m</mi><mi>l</mi><mi>n</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>h</mi><mi>t</mi><mi>t</mi><mi>p</mi><mo>:</mo><mi mathvariant="normal">/</mi><mi mathvariant="normal">/</mi><mi>w</mi><mi>w</mi><mi>w</mi><mi mathvariant="normal">.</mi><mi>w</mi><mn>3.</mn><mi>o</mi><mi>r</mi><mi>g</mi><mi mathvariant="normal">/</mi><mn>1998</mn><mi mathvariant="normal">/</mi><mi>M</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi mathvariant="normal">/</mi><mi>M</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>M</mi><mi>L</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>e</mi><mi>m</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>s</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>r</mi><mi>o</mi><mi>w</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>c</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>o</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>n</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>t</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>n</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>t</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>s</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>o</mi><mo>&gt;</mo><mo>=</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>o</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>f</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>r</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>d</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>o</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>e</mi><mi>t</mi><mi>c</mi><mi>h</mi><mi>y</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>f</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>o</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>r</mi><mi>o</mi><mi>w</mi><mo>&gt;</mo><mo>&lt;</mo><mi>a</mi><mi>n</mi><mi>n</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>o</mi><mi>d</mi><mi>i</mi><mi>n</mi><mi>g</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>a</mi><mi>p</mi><mi>p</mi><mi>l</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">/</mi><mi>x</mi><mo>−</mo><mi>t</mi><mi>e</mi><mi>x</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>c</mi><mi>o</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo>=</mo><mi>f</mi><mi>r</mi><mi>e</mi><mi>a</mi><mi>d</mi><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>a</mi><mi>n</mi><mi>n</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>e</mi><mi>m</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>s</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>k</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><mo>−</mo><mi>h</mi><mi>t</mi><mi>m</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>a</mi><mi>r</mi><mi>i</mi><mi>a</mi><mo>−</mo><mi>h</mi><mi>i</mi><mi>d</mi><mi>d</mi><mi>e</mi><mi>n</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>b</mi><mi>a</mi><mi>s</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>t</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>h</mi><mi>e</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.6151</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>c</mi><mi>o</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>n</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>t</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>n</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>t</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>s</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.2778</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>r</mi><mi>e</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>=</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.2778</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>b</mi><mi>a</mi><mi>s</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>t</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>h</mi><mi>e</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>1</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi>v</mi><mi>e</mi><mi>r</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>l</mi><mo>−</mo><mi>a</mi><mi>l</mi><mi>i</mi><mi>g</mi><mi>n</mi><mo>:</mo><mo>−</mo><mn>0.25</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.10764</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>f</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>r</mi><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>d</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>p</mi><mi>e</mi><mi>n</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mi>h</mi><mi>a</mi><mi>n</mi><mi>d</mi><mi>l</mi><mi>e</mi><mo separator="true">,</mo><mi>f</mi><mi>i</mi><mi>l</mi><mi>e</mi><mi>s</mi><mi>i</mi><mi>z</mi><mi>e</mi><mo stretchy="false">(</mo></mrow><annotation encoding="application/x-tex">filename = &quot;/usr/local/something.txt&quot;; &lt;span class=&quot;katex&quot;&gt;&lt;span class=&quot;katex-mathml&quot;&gt;&lt;math 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mathnormal&quot;&gt;e&lt;/span&gt;&lt;span class=&quot;mspace&quot; style=&quot;margin-right:0.2778em;&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mrel&quot;&gt;=&lt;/span&gt;&lt;span class=&quot;mspace&quot; style=&quot;margin-right:0.2778em;&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class=&quot;base&quot;&gt;&lt;span class=&quot;strut&quot; style=&quot;height:1em;vertical-align:-0.25em;&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot; style=&quot;margin-right:0.10764em;&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;o&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;p&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;e&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;n&lt;/span&gt;&lt;span class=&quot;mopen&quot;&gt;(&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;filename, &quot;r&quot;); &lt;span class=&quot;katex&quot;&gt;&lt;span class=&quot;katex-mathml&quot;&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding=&quot;application/x-tex&quot;&gt;contents = fread(&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;span class=&quot;katex-html&quot; aria-hidden=&quot;true&quot;&gt;&lt;span class=&quot;base&quot;&gt;&lt;span class=&quot;strut&quot; style=&quot;height:0.6151em;&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;co&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;n&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;t&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;e&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;n&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;t&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;s&lt;/span&gt;&lt;span class=&quot;mspace&quot; style=&quot;margin-right:0.2778em;&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mrel&quot;&gt;=&lt;/span&gt;&lt;span class=&quot;mspace&quot; style=&quot;margin-right:0.2778em;&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class=&quot;base&quot;&gt;&lt;span class=&quot;strut&quot; style=&quot;height:1em;vertical-align:-0.25em;&quot;&gt;&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot; style=&quot;margin-right:0.10764em;&quot;&gt;f&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;re&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;a&lt;/span&gt;&lt;span class=&quot;mord mathnormal&quot;&gt;d&lt;/span&gt;&lt;span class=&quot;mopen&quot;&gt;(&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;handle, filesize(</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mord mathnormal">nam</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">&quot;/</span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.02778em;">sr</span><span class="mord">/</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">oc</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">/</span><span class="mord mathnormal">so</span><span class="mord mathnormal">m</span><span class="mord mathnormal">e</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hin</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord">.</span><span class="mord mathnormal">t</span><span class="mord mathnormal">x</span><span class="mord mathnormal">t</span><span class="mord">&quot;</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ka</span><span class="mord mathnormal">t</span><span class="mord mathnormal">e</span><span class="mord mathnormal">x</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.0833em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ka</span><span class="mord mathnormal">t</span><span class="mord mathnormal">e</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hm</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord mathnormal">x</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">n</span><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">h</span><span class="mord mathnormal">ttp</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">//</span><span class="mord mathnormal" style="margin-right:0.02691em;">www</span><span class="mord">.</span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mord">3.</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord">/1998/</span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord">/</span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span><span class="mord mathnormal">L</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6986em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">se</span><span class="mord mathnormal">man</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">cs</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">ro</span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6986em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">h</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6986em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6986em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6986em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6986em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6986em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">o</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;=&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">m</span><span class="mord mathnormal">o</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6986em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6986em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">o</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6986em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">p</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6986em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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style="height:1em;vertical-align:-0.25em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.01968em;">ppl</span><span class="mord mathnormal">i</span><span class="mord mathnormal">c</span><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">o</span><span class="mord mathnormal">n</span><span class="mord">/</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">t</span><span class="mord mathnormal">e</span><span class="mord mathnormal">x</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">ann</span><span class="mord mathnormal">o</span><span class="mord mathnormal">t</span><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">o</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">se</span><span class="mord mathnormal">man</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">cs</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" 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mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">u</span><span class="mord mathnormal">e</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ba</span><span class="mord mathnormal">se</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">u</span><span class="mord mathnormal">t</span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">i</span><span 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style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">in</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0.2778</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ba</span><span class="mord mathnormal">se</span><span 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style="margin-right:0.02778em;">r</span><span class="mord mathnormal">u</span><span class="mord mathnormal">t</span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord mathnormal" style="margin-right:0.02778em;">er</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">c</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">−</span><span class="mord">0.25</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">in</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0.10764</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord 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style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal">re</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;=&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span 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style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">in</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0.2778</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" 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style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">u</span><span class="mord mathnormal">t</span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord mathnormal" style="margin-right:0.02778em;">er</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">c</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">−</span><span class="mord">0.25</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">in</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0.10764</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">re</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal">o</span><span class="mord mathnormal">p</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">han</span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">es</span><span class="mord mathnormal">i</span><span class="mord mathnormal">ze</span><span class="mopen">(</span></span></span></span>filename)); fclose($handle); ?>

Example #2 Binary fread() example

Warning

On systems which differentiate between binary and text files (i.e. Windows) the file must be opened with 'b' included infopen() mode parameter.

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mathvariant="normal">&quot;</mi><mi>k</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><mo>−</mo><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>m</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>x</mi><mi>m</mi><mi>l</mi><mi>n</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>h</mi><mi>t</mi><mi>t</mi><mi>p</mi><mo>:</mo><mi mathvariant="normal">/</mi><mi mathvariant="normal">/</mi><mi>w</mi><mi>w</mi><mi>w</mi><mi mathvariant="normal">.</mi><mi>w</mi><mn>3.</mn><mi>o</mi><mi>r</mi><mi>g</mi><mi mathvariant="normal">/</mi><mn>1998</mn><mi mathvariant="normal">/</mi><mi>M</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi mathvariant="normal">/</mi><mi>M</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>M</mi><mi>L</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>e</mi><mi>m</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>s</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>r</mi><mi>o</mi><mi>w</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>h</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>n</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>d</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>l</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>o</mi><mo>&gt;</mo><mo>=</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>o</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>f</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>o</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>p</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>n</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>o</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>e</mi><mi>t</mi><mi>c</mi><mi>h</mi><mi>y</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>f</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>o</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>r</mi><mi>o</mi><mi>w</mi><mo>&gt;</mo><mo>&lt;</mo><mi>a</mi><mi>n</mi><mi>n</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>o</mi><mi>d</mi><mi>i</mi><mi>n</mi><mi>g</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>a</mi><mi>p</mi><mi>p</mi><mi>l</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">/</mi><mi>x</mi><mo>−</mo><mi>t</mi><mi>e</mi><mi>x</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>h</mi><mi>a</mi><mi>n</mi><mi>d</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi>f</mi><mi>o</mi><mi>p</mi><mi>e</mi><mi>n</mi><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>a</mi><mi>n</mi><mi>n</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>e</mi><mi>m</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>s</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>k</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><mo>−</mo><mi>h</mi><mi>t</mi><mi>m</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>a</mi><mi>r</mi><mi>i</mi><mi>a</mi><mo>−</mo><mi>h</mi><mi>i</mi><mi>d</mi><mi>d</mi><mi>e</mi><mi>n</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>b</mi><mi>a</mi><mi>s</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>t</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>h</mi><mi>e</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.6944</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>h</mi><mi>a</mi><mi>n</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>d</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.01968</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>l</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.2778</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>r</mi><mi>e</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>=</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.2778</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>b</mi><mi>a</mi><mi>s</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>t</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>h</mi><mi>e</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>1</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi>v</mi><mi>e</mi><mi>r</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>l</mi><mo>−</mo><mi>a</mi><mi>l</mi><mi>i</mi><mi>g</mi><mi>n</mi><mo>:</mo><mo>−</mo><mn>0.25</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.10764</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>f</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>o</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>p</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>n</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>p</mi><mi>e</mi><mi>n</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mi>f</mi><mi>i</mi><mi>l</mi><mi>e</mi><mi>n</mi><mi>a</mi><mi>m</mi><mi>e</mi><mo separator="true">,</mo><mi mathvariant="normal">&quot;</mi><mi>r</mi><mi>b</mi><mi mathvariant="normal">&quot;</mi><mo stretchy="false">)</mo><mo separator="true">;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>k</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>k</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><mo>−</mo><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>m</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>x</mi><mi>m</mi><mi>l</mi><mi>n</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>h</mi><mi>t</mi><mi>t</mi><mi>p</mi><mo>:</mo><mi mathvariant="normal">/</mi><mi mathvariant="normal">/</mi><mi>w</mi><mi>w</mi><mi>w</mi><mi mathvariant="normal">.</mi><mi>w</mi><mn>3.</mn><mi>o</mi><mi>r</mi><mi>g</mi><mi mathvariant="normal">/</mi><mn>1998</mn><mi mathvariant="normal">/</mi><mi>M</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi mathvariant="normal">/</mi><mi>M</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>M</mi><mi>L</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>e</mi><mi>m</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>s</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>r</mi><mi>o</mi><mi>w</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>c</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>o</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>n</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>t</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>n</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>t</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>s</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>o</mi><mo>&gt;</mo><mo>=</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>o</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>f</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>r</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>i</mi><mo>&gt;</mo><mi>d</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>i</mi><mo>&gt;</mo><mo>&lt;</mo><mi>m</mi><mi>o</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>e</mi><mi>t</mi><mi>c</mi><mi>h</mi><mi>y</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>f</mi><mi>a</mi><mi>l</mi><mi>s</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>o</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>r</mi><mi>o</mi><mi>w</mi><mo>&gt;</mo><mo>&lt;</mo><mi>a</mi><mi>n</mi><mi>n</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>o</mi><mi>d</mi><mi>i</mi><mi>n</mi><mi>g</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>a</mi><mi>p</mi><mi>p</mi><mi>l</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">/</mi><mi>x</mi><mo>−</mo><mi>t</mi><mi>e</mi><mi>x</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>c</mi><mi>o</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo>=</mo><mi>f</mi><mi>r</mi><mi>e</mi><mi>a</mi><mi>d</mi><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>a</mi><mi>n</mi><mi>n</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>e</mi><mi>m</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>s</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>k</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>x</mi><mo>−</mo><mi>h</mi><mi>t</mi><mi>m</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>a</mi><mi>r</mi><mi>i</mi><mi>a</mi><mo>−</mo><mi>h</mi><mi>i</mi><mi>d</mi><mi>d</mi><mi>e</mi><mi>n</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>b</mi><mi>a</mi><mi>s</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>t</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>h</mi><mi>e</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.6151</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>c</mi><mi>o</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>n</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>t</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>n</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>t</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>s</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.2778</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>r</mi><mi>e</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>=</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.2778</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>b</mi><mi>a</mi><mi>s</mi><mi>e</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>r</mi><mi>u</mi><mi>t</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>h</mi><mi>e</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>1</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi>v</mi><mi>e</mi><mi>r</mi><mi>t</mi><mi>i</mi><mi>c</mi><mi>a</mi><mi>l</mi><mo>−</mo><mi>a</mi><mi>l</mi><mi>i</mi><mi>g</mi><mi>n</mi><mo>:</mo><mo>−</mo><mn>0.25</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mi>s</mi><mi>t</mi><mi>y</mi><mi>l</mi><mi>e</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>a</mi><mi>r</mi><mi>g</mi><mi>i</mi><mi>n</mi><mo>−</mo><mi>r</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>:</mo><mn>0.10764</mn><mi>e</mi><mi>m</mi><mo separator="true">;</mo><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>f</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>r</mi><mi>e</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>a</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>r</mi><mi>d</mi><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>n</mi><mi>o</mi><mi>r</mi><mi>m</mi><mi>a</mi><mi>l</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mi>d</mi><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mo>=</mo><mi mathvariant="normal">&quot;</mi><mi>m</mi><mi>o</mi><mi>p</mi><mi>e</mi><mi>n</mi><mi mathvariant="normal">&quot;</mi><mo>&gt;</mo><mo stretchy="false">(</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mo>&lt;</mo><mi mathvariant="normal">/</mi><mi>s</mi><mi>p</mi><mi>a</mi><mi>n</mi><mo>&gt;</mo><mi>h</mi><mi>a</mi><mi>n</mi><mi>d</mi><mi>l</mi><mi>e</mi><mo separator="true">,</mo><mi>f</mi><mi>i</mi><mi>l</mi><mi>e</mi><mi>s</mi><mi>i</mi><mi>z</mi><mi>e</mi><mo stretchy="false">(</mo></mrow><annotation encoding="application/x-tex">filename = &quot;c:\\files\\somepic.gif&quot;; &lt;span class=&quot;katex&quot;&gt;&lt;span class=&quot;katex-mathml&quot;&gt;&lt;math 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style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.0833em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ka</span><span class="mord mathnormal">t</span><span class="mord mathnormal">e</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hm</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord mathnormal">x</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">n</span><span class="mord 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class="mord">/1998/</span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord">/</span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span><span class="mord mathnormal">a</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span><span class="mord mathnormal">L</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6986em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">se</span><span class="mord mathnormal">man</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord 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class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6986em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span 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class="mord">/</span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6986em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6986em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">o</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;=&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">m</span><span class="mord mathnormal">o</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6986em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">mi</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" 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class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">u</span><span class="mord mathnormal">e</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ba</span><span class="mord mathnormal">se</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">u</span><span class="mord mathnormal">t</span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0.6944</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span 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style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">han</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">in</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0.01968</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord 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style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">in</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">i</span><span class="mord mathnormal" 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style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span 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class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6542em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">t</span><span class="mspace" 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class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ce</span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">in</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0.2778</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal">re</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;=&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">a</span><span class="mord 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style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0.2778</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ba</span><span class="mord mathnormal">se</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">u</span><span class="mord mathnormal">t</span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord mathnormal" style="margin-right:0.02778em;">er</span><span class="mord mathnormal">t</span><span class="mord mathnormal">i</span><span class="mord mathnormal">c</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">−</span><span class="mord">0.25</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">in</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">h</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0.10764</span><span class="mord mathnormal">e</span><span class="mord mathnormal">m</span><span class="mpunct">;</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">re</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">d</span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">hn</span><span class="mord mathnormal" style="margin-right:0.02778em;">or</span><span class="mord mathnormal">ma</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7335em;vertical-align:-0.0391em;"></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mord mathnormal">c</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">a</span><span class="mord mathnormal">ss</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">&quot;</span><span class="mord mathnormal">m</span><span class="mord mathnormal">o</span><span class="mord mathnormal">p</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord">&quot;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mord mathnormal">p</span><span class="mord mathnormal">an</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">han</span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">es</span><span class="mord mathnormal">i</span><span class="mord mathnormal">ze</span><span class="mopen">(</span></span></span></span>filename)); fclose($handle); ?>

Example #3 Remote fread() examples

Warning

When reading from anything that is not a regular local file, such as streams returned when reading remote files or frompopen() and fsockopen(), reading will stop after a packet is available. This means that you should collect the data together in chunks as shown in the examples below.

<?php // For PHP 5 and up $handle = fopen("http://www.example.com/", "rb"); <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>c</mi><mi>o</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo>=</mo><mi>s</mi><mi>t</mi><mi>r</mi><mi>e</mi><mi>a</mi><msub><mi>m</mi><mi>g</mi></msub><mi>e</mi><msub><mi>t</mi><mi>c</mi></msub><mi>o</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo stretchy="false">(</mo></mrow><annotation encoding="application/x-tex">contents = stream_get_contents(</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6151em;"></span><span class="mord mathnormal">co</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal">t</span><span class="mord mathnormal">re</span><span class="mord mathnormal">a</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">g</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mord mathnormal">e</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">c</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal">o</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span><span class="mord mathnormal">e</span><span class="mord mathnormal">n</span><span class="mord mathnormal">t</span><span class="mord mathnormal">s</span><span class="mopen">(</span></span></span></span>handle); fclose($handle); ?>

`<?php
$handle = fopen("http://www.example.com/", "rb");
if (FALSE === $handle) {
exit("Failed to open stream to URL");
}$contents = '';

while (!

feof($handle)) { contents.=fread(contents .= fread(contents.=fread(handle, 8192);
}
fclose($handle);
?> `

Notes

Note:

If you just want to get the contents of a file into a string, usefile_get_contents() as it has much better performance than the code above.

Note:

Note that fread() reads from the current position of the file pointer. Use ftell() to find the current position of the pointer and rewind() to rewind the pointer position.

See Also