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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 510;
int n;
ll a[2][N][N], f[N][N];
ll sum[2][N][N];

ll getsum(int sig, int a,int b, int x, int y) {
	//(a,x) (b,y)
	swap(x, b);
	if (a <= x && b <= y)
		return sum[sig][x][y] - sum[sig][a - 1][y] - sum[sig][x][b - 1] + sum[sig][a - 1][b - 1];
	else return 0;
}

ll ss;
int main() {
	cin>>n;
	for(int i = 1; i <= n; i++) {
		for(int j = 1; j <= n; j++) {
			if (i != j) {
				scanf("%lld\n", &a[i<j][i][j]), ss += a[i<j][i][j];
			}
		}
	}
	for(int o=0;o<2;o++) {
		for(int i = 1; i <= n; i++) {
			for(int j = 1; j <= n; j++) {
				sum[o][i][j] = sum[o][i][j - 1] + a[o][i][j];
			}
		}

		for(int i = 1; i <= n; i++) {
			for(int j = 1; j <= n; j++) {
				sum[o][i][j] += sum[o][i - 1][j];
			}
		}
	}

	memset(f,128,sizeof f);
	ll ans = f[0][0];
	f[0][0] = 0;
	for(int l = 0; l <= n; l++) {
		for(int r = l; r <= n; r++) {
			for(int nx = r + 1; nx <= n; nx++) {
				if (r == 0 && nx == 2) {
					int kk = r;
				}
				f[r][nx] = max(f[r][nx], f[l][r] + getsum(1, 1, r, r + 1, nx) + getsum(0, r + 1, nx, l + 1, nx));

			}
		}
	}
	for(int l = 1; l <= n; l++) ans = max(ans, f[l][n]);
	cout<<ss - ans<<endl;
}