<?php
function stack_machine_emulator ( $S ) {

    $raw_string = str_split($S);
    $stack_array = array();

    foreach ($raw_string as $value)
    {
        if (is_numeric($value))
        {
            $stack_array[] = $value;
        }

        if ($value == '+')
        {
            $value1 = array_pop($stack_array);
            $value2 = array_pop($stack_array);

            $added = $value1 + $value2;

            $stack_array[] = $added;
        }

        if ($value == '*')
        {
            $value1 = array_pop($stack_array);
            $value2 = array_pop($stack_array);

            $multiplied = $value1 * $value2;

            $stack_array[] = $multiplied;
        }
    }

    return $stack_array[0];
}