Let's consider an $*n* × *n*$ square matrix, consisting of digits one and zero.

We'll consider a matrix good, if it meets the following condition: in each row of the matrix all ones go in one group. That is, each row of the matrix looks like that $00...0011...1100...00$ (or simply consists of zeroes if it has no ones).

You are given matrix $*a*$ of size $*n* × *n*$, consisting of zeroes and ones. Your task is to determine whether you can get a good matrix $*b*$ from it by rearranging the columns or not.

Input

The first line contains integer $*n*$ ($1 ≤ *n* ≤ 500$) — the size of matrix $*a*$.

Each of $*n*$ following lines contains $*n*$ characters "0" and "1" — matrix $*a*$. Note that the characters are written without separators.

Output

Print "YES" in the first line, if you can rearrange the matrix columns so as to get a good matrix $*b*$. In the next $*n*$ lines print the good matrix $*b*$. If there are multiple answers, you are allowed to print any of them.

If it is impossible to get a good matrix, print "NO".