Matrix

Time Limit: Java: 2000 ms / Others: 2000 ms

Memory Limit: Java: 65536 KB / Others: 65536 KB

Description

Given an n*n matrix A, whose entries Ai,j are integer numbers ( 0 <= i SHIFT at row i ( 0 <= i

You can do the SHIFT operation at arbitrary row, and as many times as you like. Your task is to minimize


Input

The input consists of several test cases. The first line of each test case contains an integer n. Each of the following n lines contains n integers, indicating the matrix A. The input is terminated by a single line with an integer -1. You may assume that 1 <= n <= 7 and |Ai,j| 4.


Output

For each test case, print a line containing the minimum value of the maximum of column sums.


Sample Input

2
4 6
3 7
3
1 2 3
4 5 6
7 8 9
-1

Sample Output

11
15

Hint

None

Source

Asia 2004, Shanghai (Mainland China), Prelimi

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