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>
using namespace std;
long long f[510][510],a[510][510],b[510][510];
inline long long mymin(long long x,long long y){return x<y?x:y;}
inline long long CVN(int ll,int lr,int rl,int rr){return a[lr][rr]-a[ll-1][rr]-a[lr][rl-1]+a[ll-1][rl-1];}
int main()
{
	int n;scanf("%d",&n);
	memset(a,0,sizeof(a));
	memset(b,0,sizeof(b));
	for(int i=1;i<=n;i++)
	{
		for(int j=1;j<=n;j++)
		{
			if(i==j)continue;
			int c;scanf("%d",&c);
			a[i][j]=a[i-1][j]+a[i][j-1]+c-a[i-1][j-1];
		}
	}
	for(int j=2;j<=n;j++)
	{
		for(int i=1;i<j;i++)b[i][j]=b[i][j-1]+CVN(i,j-1,j,j);
	}
	memset(f,63,sizeof(f));f[0][1]=0;
	for(int i=0;i<n;i++)
	{
		for(int j=i+1;j<=n;j++)
		{
			for(int k=j+1;k<=n+1;k++)
			{
				f[j][k]=mymin(f[j][k],f[i][j]+b[j][k-1]+CVN(k,n,i,j-1));
			}
		}
	}
	long long ss=0x3f3f3f3f3f3f3f3fll;
	for(int i=1;i<=n;i++)if(f[i][n+1]<ss)ss=f[i][n+1];
	printf("%lld\n",ss);
	return 0;
}