Magic Matrix

A magic matrix is an N×M rectangle that contains all values in [1, N*M] exactly once, in any order.
Your task is to generate a 16×16 matrix that contains at least 800 magic submatrices.

Note: you will receive full feedback on your submissions, including the number of magic submatrices.

Output

The output should contain 16 lines, each of them containing 16 values between 1 and 16².

Sample

Output

Explanation

1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

This matrix has 257 magic submatrices.
253 of them contain a single value, 1.
The others are:

1 2

2 1

1 2 4 3

2 3 1

Note that this output is not considered correct,
because it contains less than 800 magic submatrices.