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>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <vector>
#include <iomanip>
#include <iostream> 
#define ll long long
#define N 550
#define inf 1000000000000000
using namespace std;

ll n,dp[N][N],w[N][N],p[N][N],tot[N][N];

inline ll getans(int a,int b,int c,int d){
	return p[b][d]-(c==0?0:p[b][c-1])-(a==0?0:p[a-1][d])+(a==0||c==0?0:p[a-1][c-1]);
}

void fl()
{
	freopen("park.in","r",stdin);
	freopen("park.out","w",stdout);
}

int main()
{
	//fl();
	cin>>n;
	for (int i=1;i<=n;i++)
		for (int j=1;j<=n;j++) 
			if (i!=j) cin>>w[i][j];
	for (int i=1;i<=n;i++)
		for (int j=1;j<=n;j++)
			p[i][j]=p[i-1][j]+p[i][j-1]-p[i-1][j-1]+w[i][j];
	for (int i=1;i<=n;i++)
		for (int j=1;j<=n;j++)
			tot[i][j]=tot[i-1][j]+tot[i][j-1]-tot[i-1][j-1]+(i<j?w[i][j]:0);
	for (int i=1;i<=n;i++)
	{
		dp[i][1]=tot[i][i]-tot[0][i]-tot[i][0]+tot[0][0];
		for (int j=2;j<=i;j++)
		{
			dp[i][j]=inf;
			for (int k=1;k<j;k++)
				dp[i][j]=min(dp[i][j],dp[j-1][k]+(tot[i][i]-tot[i][j-1]-tot[j-1][i]+tot[j-1][j-1])+getans(j,i,0,k-1));
		}
	}
	ll ans=inf;
	for (int i=1;i<=n;i++) ans=min(ans,dp[n][i]);
	cout<<ans<<endl;
	return 0;
}