Magic Squares are square arrays of numbers that have the interesting property that the numbers in each column, and in each row, all add up to the same total.

Given a 4×4 square of numbers, determine if it is a magic square.

Input Specification

The input consists of four lines, each line having 4 space-separated integers.

Output Specification

Output either magic if the input is a magic square, or not magic if the input is not a magic square.

Sample Input 1

16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1

Output for Sample Input 1

magic

Explanation for Output for Sample Input 1

Notice that each row adds up to 34, and each column also adds up to 34.

Sample Input 2

5 10 1 3
10 4 2 3
1 2 8 5
3 3 5 0

Output for Sample Input 2

not magic