0 or 1

Given a n*n matrix C _ij (1<=i,j<=n),We want to find a n*n matrix X _ij (1<=i,j<=n),which is 0 or 1.

Besides,X _ij meets the following conditions:

1.X ₁₂+X ₁₃+...X _1n=1
2.X _1n+X _2n+...X _n-1n=1
3.for each i (1<i<n), satisfies ∑X _ki (1<=k<=n)=∑X _ij (1<=j<=n).

For example, if n=4,we can get the following equality:

X ₁₂+X ₁₃+X ₁₄=1
X ₁₄+X ₂₄+X ₃₄=1
X ₁₂+X ₂₂+X ₃₂+X ₄₂=X ₂₁+X ₂₂+X ₂₃+X ₂₄
X ₁₃+X ₂₃+X ₃₃+X ₄₃=X ₃₁+X ₃₂+X ₃₃+X ₃₄

Now ,we want to know the minimum of ∑C _ij*X _ij(1<=i,j<=n) you can get.

The input consists of multiple test cases (less than 35 case).
For each test case ,the first line contains one integer n (1<n<=300).
The next n lines, for each lines, each of which contains n integers, illustrating the matrix C, The j-th integer on i-th line is C _ij(0<=C _ij<=100000).

For each case, output the minimum of ∑C _ij*X _ij you can get.