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
// D - Negative Cycle
#include <bits/stdc++.h>

using namespace std;

#define	INF	1e16

int main(int argc, char *argv[])
{
	ios::sync_with_stdio(false); cin.tie(0);

	int n;
	cin >> n;
	vector<vector<long long> > a(n, vector<long long>(n));
	for (int i = 0; i < n; i++)
		for (int j = 0; j < n; j++)
			if (i != j) cin >> a[i][j];

	vector<vector<long long> > dp(n + 1, vector<long long>(n + 1, INF));
	dp[0][0] = 0;

	for (int i = 1; i <= n; i++) {
		vector<long long> x(i), y(i);
		for (int j = 0; j < i; j++) {
			for (int k = i + 1; k <= n; k++) x[j] += a[k - 1][j - 1];
			if (j > 0) x[j] += x[j - 1];
		}
		for (int j = i - 1; j >= 0; j--) {
			for (int k = j + 1; k < i + 1; k++) y[j] += a[j][k - 1];
			if (j + 1 < i - 1) y[j] += y[j + 1];
		}
		for (int j = 0; j < i; j++)
			for (int k = 0; k < j + 1; k++)
				dp[i][j] = min(dp[i][j], dp[j][k] + x[j] - x[k] + y[j]);
	}

	cout << *min_element(dp[n].begin(),dp[n].end()) << endl;

	return 0;
}
