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<cstring>
#include<algorithm>
#include<cmath>
#define maxn 505
#define ll long long 
using namespace std;
	
int n,i,j,k,s[maxn][maxn];
ll a[maxn][maxn],b[maxn][maxn],f[maxn][maxn];

ll Suma(int x,int xx,int y,int yy){
	if (x>xx||y>yy) return 0;
	return a[xx][yy]-a[x-1][yy]-a[xx][y-1]+a[x-1][y-1];
}

ll Sumb(int l,int r){
	return b[r][r]-b[r][l-1]-b[l-1][r]+b[l-1][l-1];
}
	
int main(){
	scanf("%d",&n);
	for(i=1;i<=n;i++){
		for(j=1;j<i;j++) scanf("%d",&a[i][j]);
		for(j=i+1;j<=n;j++) scanf("%d",&a[i][j]);
		for(j=1;j<=n;j++) s[i][j]=a[i][j];
	}
	for(i=1;i<=n;i++) for(j=1;j<=n;j++) 
		b[i][j]=a[i][j]*(i<j)+b[i-1][j]+b[i][j-1]-b[i-1][j-1];
	for(i=1;i<=n;i++) for(j=1;j<=n;j++)
		a[i][j]+=a[i-1][j]+a[i][j-1]-a[i-1][j-1];
	memset(f,127,sizeof(f)),f[0][0]=0;
	for(i=0;i<n;i++) for(j=0;j<=i;j++) if (f[i][j]<1e18){
		for(k=i+1;k<=n;k++)
			f[k][i]=min(f[k][i],f[i][j]+Sumb(i+1,k)+Suma(i+1,k,1,j));
	}
	ll ans=1e18;
	for(i=0;i<=n;i++) ans=min(ans,f[n][i]);
	printf("%lld\n",ans);
}