Practice 2D array with the exercise "Magic Square"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

2D array

Statement

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

Constraints

Example

Input

Output

MAGIC

Solve it

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