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;

using ll = long long;

int main(){
	ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
	int n;
	cin >> n;
	n += 1;
	vector<vector<ll> > a(n, vector<ll>(n, 0));
	for(int i = 1; i < n; i++){
		for(int j = 1; j < n; j++){
			if(i == j) continue;
			cin >> a[i][j];
		}
	}
	vector<vector<ll> > rsum(n, vector<ll>(n, 0));
	vector<vector<ll> > lsum(n, vector<ll>(n, 0));
	for(int i = 0; i < n; i++){
		for(int j = i+1; j < n; j++){
			rsum[i][j] = rsum[i][j-1];
			lsum[i][j] = lsum[i][j-1];
			for(int k = i; k < j; k++){
				rsum[i][j] += a[k][j];
				lsum[i][j] += a[j][k];
			}
		}
	}
	vector<vector<ll> > dp(n, vector<ll> (n, 2e18));
	dp[0][0] = 0;
	for(int j = 0; j < n; j++){
		for(int i = 0; i <= j; i++){
			for(int k = j+1; k < n; k++){
				ll newdp = dp[i][j];
				newdp += rsum[j+1][k];
				newdp += lsum[0][k] - lsum[0][j] - lsum[i][k] + lsum[i][j];
				dp[j+1][k] = min(dp[j+1][k], newdp);
			}
		}
	}
	ll ans = 2e18;
	for(int i = 0; i < n; i++){
		ans = min(ans, dp[i][n-1]);
	}
	cout << ans << '\n';
}