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 <iostream>

using i64 = long long;

const int N = 500 + 7;

int n;
i64 a[N][N], f[N][N], g[N][N], h[N][N], ans;

i64 s(i64 f[N][N], int i1, int i2, int j1, int j2) {
	return f[i2][j2] + f[i1][j1] - f[i2][j1] - f[i1][j2];
}

int main() {
//	freopen("code.in", "r", stdin);
//	freopen("code.out", "w", stdout);

	scanf("%d", &n);
	for (int i = 1; i <= n; ++i)
		for (int j = 1; j <= n; ++j) {
			if (i != j) scanf("%lld", a[i] + j);
			(i < j ? f[i][j] : g[j][i]) = a[i][j];
		}
	for (int i = 1; i <= n; ++i)
		for (int j = 1; j <= n; ++j)
			f[i][j] += f[i - 1][j] + f[i][j - 1] - f[i - 1][j - 1],
			g[i][j] += g[i - 1][j] + g[i][j - 1] - g[i - 1][j - 1];
	ans = s(g, 0, n, 0, n);
	for (int i = 1; i < n; ++i) {
		h[i][0] = s(f, 0, i, i, i + 1) + s(g, 0, i, 0, i + 1);
		for (int j = 1; j < i; ++j)
			for (int k = 0; k < j; ++k)
				h[i][j] = std::max(h[i][j], h[j][k] + s(f, 0, i, i, i + 1) + s(f, 0, j, j + 1, i) + s(g, j, i, i, i + 1) + s(g, k, i, j + 1, i) );
	}
	for (int i = 1; i < n; ++i)
		for (int j = 0; j < i; ++j)
			ans = std::max(ans, h[i][j] + s(f, 0, i, i + 1, n) + s(g, j, n, i + 1, n));
	printf("%lld\n", s(f, 0, n, 0, n) + s(g, 0, n, 0, n) - ans);
	return 0;
}
