<?php
$lines = file('input', FILE_IGNORE_NEW_LINES | FILE_SKIP_EMPTY_LINES);

$mapings         = [];
$before          = [];
$initialMappings = [];
$template        = array_shift($lines);
for ($i = 0; $i < strlen($template) - 1; $i++) {
    $pair          = substr($template, $i, 2);
    $before[$pair] = 1;
}
foreach ($lines as $item) {
    $line                      = explode(' -> ', $item);
    $mapings[$line[0]]         = $line[1];
    $initialMappings[$line[0]] = 0;
}

for ($step = 1; $step <= 40; $step++) {
    $after = $initialMappings;
    foreach ($before as $pair => $count) {
        $left  = $pair[0] . $mapings[$pair];
        $right = $mapings[$pair] . $pair[1];
        $after[$left]  += $count;
        $after[$right] += $count;
    }
    $before = $after;
}
$letters = [];
foreach ($before as $pair => $count) {
    $left = $pair[0];
    if (!isset($letters[$left])) {
        $letters[$left] = 0;
    }
    $letters[$left] += $count;
}
$letters[substr($template, -1)] += 1;
sort($letters);

echo array_pop($letters) - array_shift($letters); //2516901104210