Pro.ID10254 TitleHomogeneous Squares Title链接http://10.20.2.8/oj/exercise/problem?problem_id=10254 AC0 Submit0 Ratio- 时间&空间限制描述Assume you have a square of size n that is divided into n × n positions just as a checkerboard. Two positions (x1, y1) and (x2, y2), where 1 ≤ x1, y1, x2, y2 ≤ n, are called "independent" if they occupy different rows and different columns, that is, x1 ≠ x2 and y1 ≠ y2. More generally, n positions are called independent if they are pairwise independent. It follows that there are n! different ways to choose n independent positions. Assume further that a number is written in each position of such an n × n square. This square is called "homogeneous" if the sum of the numbers written in n independent positions is the same, no matter how the positions are chosen. Write a program to determine if a given square is homogeneous! 输入The input contains several test cases. The first line of each test case contains an integer n (1 ≤ n ≤ 1000). Each of the next n lines contains n numbers, separated by exactly one space character. Each number is an integer from the interval [-1000000, 1000000]. The last test case is followed by a zero. 输出Description Assume you have a square of size n that is divided into n × n positions just as a checkerboard. Two positions (x1, y1) and (x2, y2), where 1 ≤ x1, y1, x2, y2 ≤ n, are called "independent" if they occupy different rows and different columns, that is, x1 ≠ x2 and y1 ≠ y2. More generally, n positions are called independent if they are pairwise independent. It follows that there are n! different ways to choose n independent positions. Assume further that a number is written in each position of such an n × n square. This square is called "homogeneous" if the sum of the numbers written in n independent positions is the same, no matter how the positions are chosen. Write a program to determine if a given square is homogeneous! Input The input contains several test cases. The first line of each test case contains an integer n (1 ≤ n ≤ 1000). Each of the next n lines contains n numbers, separated by exactly one space character. Each number is an integer from the interval [-1000000, 1000000]. The last test case is followed by a zero. Output For each test case output whether the specified square is homogeneous or not. Adhere to the format shown in the sample output. Sample Input 2 Sample Output homogeneous Source 样例输入2 样例输出homogeneous 作者 |