bash-pure, 289 bytes

Result

AC

Code [DL]

a=()
while read -n 1 c; do
a+=($c)
done
q(){
local k i s=() l=()
p=()
(($#==0))&&return 0
k=$1
shift
for i; do
if [[ $i < $k ]]; then
s+=("$i")
else
l+=("$i")
fi
done
q "${s[@]}"
s=("${p[@]}")
q "${l[@]}"
l=("${p[@]}")
p=("${s[@]}" "$k" "${l[@]}")
}
q "${a[@]}"
echo $(IFS=;echo "${p[*]}")

stdin

3138330507774457265599812563591160078846996290555463511670437760728604417528595241812576016893357210

stdout

0000000000111111111112222222233333333344444444555555555555555666666666667777777777778888888899999999

stderr

/bin/bash: warning: setlocale: LC_ALL: cannot change locale (en_US.UTF-8)

strace