Sorting Strings

The score of a lowercase English string $S$ is the sum of the squares of the frequencies of its letters. For example, abaca has score $3^2+1^2+1^2=11$.

Sort the $N$ strings $S_1,\ldots,S_N$ by the following rules.

1. A smaller score comes first.
2. For equal scores, a shorter string comes first.
3. For equal scores and lengths, lexicographically smaller strings come first. Lexicographic order is dictionary order; for example, abc precedes abd.

Repeated strings must be printed as many times as they occur in the input.

The input is given in the following format.

$N$ $S_1$ $S_2$

Print the sorted strings on $N$ lines, one string per line.

• $1 \leq N \leq 50\,000$.
• $1\leq |S_i|\leq20$ ().