A8866 | Matrix

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.

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.

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".