문제
크기가 n이고, 체커보드처럼 n×n개의 칸으로 나누어져 있는 정사각형이 있다. 1 ≤ x1, y1, x2, y2 ≤ n 을 만족하는 두 위치 (x1, y1)와 (x2, y2)가 독립이 되려면, 서로 다른 행과 열을 차지하고 있어야 한다. 즉, x1 ≠ x2, y1 ≠ y2가 되어야 한다.n개의 위치가 독립일 되려면, 모든 쌍이 독립이 되어야 한다. 즉, 서로 다른 n개의 위치를 독립이 되도록 고르는 방법의 수는 총 n!개이다.
정사각형의 각 칸에 숫자가 쓰여 있다. 이 정사각형이 동차 정사각형이 되려면, n개의 독립적인 위치에 쓰여 있는 숫자의 합이 고르는 방법과 상관없이 항상 같아야 한다.
정사각형에 쓰여 있는 숫자가 주어졌을 때, 동차 정사각형인지 아닌지를 구하는 프로그램을 작성하시오.
출력
각 테스트 케이스에 대해서, 동차 정사각형이라면 "homogeneous"를, 아니라면 "not homogeneous"를 출력한다.
예제 출력 1
복사
homogeneous
not homogeneous
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