
58  The 7th Zhejiang University Programming Contests  1002
In recreational mathematics, a magic square of ndegree is an arrangement of n^{2} numbers, distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. For example, the picture below shows a 3degree magic square using the integers of 1 to 9. Given a finished number square, we need you to judge whether it is a magic square. Input The input contains multiple test cases. The first line of each case stands an only integer N (0 < N < 10), indicating the degree of the number square and then N lines follows, with N positive integers in each line to describe the number square. All the numbers in the input do not exceed 1000. A case with N = 0 denotes the end of input, which should not be processed. Output For each test case, print "Yes" if it's a magic square in a single line, otherwise print "No". Sample Input 2 1 2 3 4 2 4 4 4 4 3 8 1 6 3 5 7 4 9 2 4 16 9 6 3 5 4 15 10 11 14 1 8 2 7 12 13 0 Sample Output No No Yes Yes 