## Goal

A magic square is a n×n square grid (where n is the number of cells on each side) filled with distinct positive integers in the range 1, 2 …, n² such that each cell contains a different integer and the sum of the integers in each row, column and diagonal is equal. The sum is called the magic constant or magic sum of the magic square. Print MAGIC if the given square is magic or else MUGGLE.
Input

**Line 1 :** n

`n` lines : A line of the square

Output

**Line 1 :** MAGIC or MUGGLE

Example

Input

3
2 7 6
9 5 1
4 3 8