Description

Sort the binary strings first by length, then by the number of $1$'s if lengths are equal, and finally by ASCII value (lexicographical order) if the number of $1$'s is also equal.

Input Format

The first line contains an integer $n$ ($1≤n≤100$), representing the number of strings.
The input data contains some binary strings, with each string's length not exceeding $256$ characters.

Output Format

Rearrange the order of the binary strings according to the sorting rules described above, and output them in sequence.

Sample

6
10011111
00001101
1010101
1
0
1100

0
1
1100
1010101
00001101
10011111