#!/usr/bin/env bash
read w h d s
r=$(bc<<<"scale=5;($d^4 / $h^4 - 1) * $h * $w * 3 / 13 / (1 + $s)")
r=${r#-}
q=$(bc<<<"scale=5;sqrt($r)")
t="$(for i in $(seq 1 ${q%%.*}); do
m=$(bc<<<"scale=5;$r/$i")
echo "${m##*.}|$i: $m"
done | sort -n | cut -d\| -f2-)"
echo -e "\nsqrt = $q\n"
head -15 <<<"$t"
echo ""
tail -15 <<<"$t"
IyEvdXNyL2Jpbi9lbnYgYmFzaAoKcmVhZCB3IGggZCBzCnI9JChiYzw8PCJzY2FsZT01OygkZF40IC8gJGheNCAtIDEpICogJGggKiAkdyAqIDMgLyAxMyAvICgxICsgJHMpIikKcj0ke3IjLX0KcT0kKGJjPDw8InNjYWxlPTU7c3FydCgkcikiKQp0PSIkKGZvciBpIGluICQoc2VxIDEgJHtxJSUuKn0pOyBkbwogICAgbT0kKGJjPDw8InNjYWxlPTU7JHIvJGkiKQogICAgZWNobyAiJHttIyMqLn18JGk6ICRtIgpkb25lIHwgc29ydCAtbiB8IGN1dCAtZFx8IC1mMi0pIgplY2hvIC1lICJcbnNxcnQgPSAkcVxuIgpoZWFkIC0xNSA8PDwiJHQiCmVjaG8gIiIKdGFpbCAtMTUgPDw8IiR0Igo=