common ancestor in file list

#!/bin/bash -eu
list=$(mktemp)
trap 'rm -f -- ${list}' EXIT
cat - >${list}
n=$(wc -l <${list})
dir=$(head -1 ${list} | xargs dirname)
while (( n != $(find ${dir} -type f | wc -l) )); do dir=$(dirname ${dir}); done
echo $(basename ${dir})
exit