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 square of numbers, determine if it is a magic square.
输入格式
The input consists of four lines, each line having space-separated integers.
输出格式
Output either magic if the input is a magic square, or not magic if the input is not a magic square.
样例
样例输入 1
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
样例输出 1
magic
样例输入 2
5 10 1 3
10 4 2 3
1 2 8 5
3 3 5 0
样例输出 2
not magic
数据范围与提示
Explanation for Output for Sample Input 1
Notice that each row adds up to , and each column also adds up to .
Explanation for Output for Sample Input 2
Notice that the top row adds up to , but the rightmost column adds up to .
