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>
#include<vector>
#include<algorithm>
#include<string.h>
#define int long long
using namespace std;
const int N=502;
const int inf=1e15+2;
int ar[N][N],dp[N][N],sum[N][N],f[N][N],damn[N][N];
signed main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	int n,i,j,k,l,ans=inf,xd=0;
	cin>>n;
	for(i=1;i<=n;i++){
		for(j=1;j<=n;j++){
			if(i==j){
				continue;
			}
			cin>>ar[i][j];
			sum[i][j]=sum[i][j-1]+ar[i][j];
			xd+=ar[i][j];
		}
	}
//	cout<<"cac"<<endl;
	for(i=1;i<=n;i++){
		for(j=0;j<=n;j++){
			dp[i][j]=inf;
		}
		dp[0][i]=inf;
		for(j=i;j<=n;j++){
			for(k=1;k<=n;k++){
				damn[i][j]+=sum[k][j]-sum[k][i-1];	
			}
			f[i][j]=f[i][j-1];
			for(k=i;k<j;k++){
				f[i][j]+=ar[k][j];
			}
		}
	}
//	cout<<"cac"<<endl;
	for(i=1;i<=n;i++){
		for(j=1;j<=n;j++){
			for(k=j;k<=n;k++){
				damn[j][k]-=sum[i][k]-sum[i][j-1];
			}
		}
		for(j=0;j<i;j++){
			for(k=0;k<=j;k++){
				dp[i][j]=min(dp[i][j],dp[j][k]+damn[k+1][j]+f[j+1][i]);
			}
			if(i==n){
				ans=min(ans,dp[i][j]);
			}
		}
	}
	cout<<ans;
}