The square matrix is given. Find the inverse matrix.

Input

The first line contains the size of the matrix n (1 ≤ n ≤ 100). Each of the next n lines contains n real numbers - the data of the matrix.

Output

If the inverse matrix does not exist print NO. Otherwise print YES in the first line, and then print n lines with n real numbers in each - the inverse matrix. The answer is correct if the relative error is no more than 10-6.