In recreational mathematics, a magic square of n-degree is an arrangement of n2 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 3-degree 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
