Inverse matrix#5469

Inverse matrix

2 seconds
64 megabytes
Very hard

You are given a square matrix.

Your task is to find its inverse.

Input

The first line contains a single integer (1 \le N \le 100) — the size of the matrix. The next lines each contain real numbers, which represent the matrix.

Output

If the inverse of the matrix does not exist, output a single line with the word NO. Otherwise, output YES on the first line, followed by lines, each containing real numbers representing the inverse matrix.

Examples

Example 1

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