#!/bin/bash

rules=()
n_step=40
declare -A polymer
declare -A occurences
read line
occurences[${line:0:1}]=$((${occurences[${line:0:1}]}+1))
for ((i=1; i<${#line}; i++)); do
  pair=${line:$((i-1)):2}
  polymer[$pair]=$((${polymer[$pair]}+1))
  occurences[${line:$i:1}]=$((${occurences[${line:$i:1}]}+1))
done
read

while read line; do
  rules+=( ${line% ->*}'|'${line#*-> } )
done

for ((i=0; i<$n_step; i++)); do
  declare -A new_polymer
  for rule in ${rules[@]}; do
    rule_pair=${rule:0:2}
    rule_pair_1=${rule:0:1}${rule:3:1}
    rule_pair_2=${rule:3:1}${rule:1:1}
    if ! [ -v polymer[$rule_pair] ]; then
      polymer[$rule_pair]=0
    fi
    new_polymer[$rule_pair]=$((${new_polymer[$rule_pair]}-${polymer[$rule_pair]}))
    new_polymer[$rule_pair_1]=$((${new_polymer[$rule_pair_1]}+${polymer[$rule_pair]}))
    new_polymer[$rule_pair_2]=$((${new_polymer[$rule_pair_2]}+${polymer[$rule_pair]}))
    occurences[${rule:3:1}]=$((${occurences[${rule:3:1}]}+${polymer[$rule_pair]}))
  done
  for new_pair in ${!new_polymer[@]}; do
    if ! [ -v polymer[$new_pair] ]; then
      polymer[$new_pair]=0
    fi
    polymer[$new_pair]=$((${polymer[$new_pair]}+${new_polymer[$new_pair]}))
  done
  unset new_polymer
done

occurences_array=( $(printf "%s\n" "${occurences[@]}" | sort -nr) )
echo $((occurences_array[0]-occurences_array[-1]))