We have a weighted directed graph with N vertices numbered 0 to N-1.

The graph initially has N-1 edges. The i-th edge (0 \leq i \leq N-2) is directed from Vertex i to Vertex i+1 and has a weight of 0.

Snuke will now add a new edge (i → j) for every pair i, j (0 \leq i,j \leq N-1,\ i \neq j). The weight of the edge will be -1 if i < j, and 1 otherwise.

Ringo is a boy. A negative cycle (a cycle whose total weight is negative) in a graph makes him sad. He will delete some of the edges added by Snuke so that the graph will no longer contain a negative cycle. The cost of deleting the edge (i → j) is A_{i,j}. He cannot delete edges that have been present from the beginning.

Find the minimum total cost required to achieve Ringo's objective.

Constraints

* 3 \leq N \leq 500
* 1 \leq A_{i,j} \leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_{0,1} A_{0,2} A_{0,3} \cdots A_{0,N-1}
A_{1,0} A_{1,2} A_{1,3} \cdots A_{1,N-1}
A_{2,0} A_{2,1} A_{2,3} \cdots A_{2,N-1}
\vdots
A_{N-1,0} A_{N-1,1} A_{N-1,2} \cdots A_{N-1,N-2}


Output

Print the minimum total cost required to achieve Ringo's objective.

Examples

Input

3
2 1
1 4
3 3


Output

2


Input

4
1 1 1
1 1 1
1 1 1
1 1 1


Output

2


Input

10
190587 2038070 142162180 88207341 215145790 38 2 5 20
32047998 21426 4177178 52 734621629 2596 102224223 5 1864
41 481241221 1518272 51 772 146 8805349 3243297 449
918151 126080576 5186563 46354 6646 491776 5750138 2897 161
3656 7551068 2919714 43035419 495 3408 26 3317 2698
455357 3 12 1857 5459 7870 4123856 2402 258
3 25700 16191 102120 971821039 52375 40449 20548149 16186673
2 16 130300357 18 6574485 29175 179 1693 2681
99 833 131 2 414045824 57357 56 302669472 95
8408 7 1266941 60620177 129747 41382505 38966 187 5151064


Output

2280211
#include <cstdio>
#include <algorithm>

typedef long long LL;
const LL Infll = 0x3f3f3f3f3f3f3f3f;
const int MN = 505;

int N;
LL A[MN][MN], B[MN][MN], f[MN][MN], Ans;

inline LL val(int k, int j, int i) {
	return B[j + 1][i] + A[N][j] - A[N][k] - A[i][j] + A[i][k];
}

int main() {
	scanf("%d", &N), Ans = Infll;
	for (int i = 1; i <= N; ++i)
		for (int j = 1; j <= N; ++j)
			if (j != i) scanf("%lld", &A[i][j]);
	for (int j = 1; j <= N; ++j)
		for (int i = j; i >= 1; --i)
			B[i][j] = B[i + 1][j] + B[i][j - 1] - B[i + 1][j - 1] + A[i][j];
	for (int i = 1; i <= N; ++i)
		for (int j = 1; j <= N; ++j)
			A[i][j] += A[i - 1][j] + A[i][j - 1] - A[i - 1][j - 1];
	for (int i = 1; i <= N - 1; ++i) {
		f[i][0] = val(0, 0, i);
		Ans = std::min(Ans, f[i][0] + val(0, i, N));
		for (int j = 1; j < i; ++j) {
			f[i][j] = Infll;
			for (int k = 0; k < j; ++k)
				f[i][j] = std::min(f[i][j], f[j][k] + val(k, j, i));
			Ans = std::min(Ans, f[i][j] + val(j, i, N));
		}
	}
	printf("%lld\n", Ans);
	return 0;
}