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<cstdio>
#include<cstring>
using namespace std;
const int N=505;
const long long INF=4557430888798830399;
int n;
long long a[N][N];
long long s1[N][N],s2[N][N];
long long f[N][N];
long long calc1(int l1,int r1,int l2,int r2)
{
	swap(l1,l2);
	swap(r1,r2);
	if(l1>r1) return 0;
	if(l2>r2) return 0;
//	cerr<<"Calc1"<<l1<<" "<<r1<<" "<<l2<<" "<<r2<<" res:"<<s1[r1][r2]<<"\n";
	return s1[r1][r2]-s1[l1-1][r2]-s1[r1][l2-1]+s1[l1-1][l2-1];
}
long long calc2(int l1,int r1,int l2,int r2)
{
	if(l1>r1) return 0;
	if(l2>r2) return 0;
//	cerr<<"Calc-1"<<l1<<" "<<r1<<" "<<l2<<" "<<r2<<" res:"<<s2[r1][r2]-s2[l1-1][r2]-s2[r1][l2-1]+s2[l1-1][l2-1]<<"\n";
	return s2[r1][r2]-s2[l1-1][r2]-s2[r1][l2-1]+s2[l1-1][l2-1];
}
int main()
{
//	freopen("data.in","r",stdin);
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
		for(int j=1;j<=n;j++)
			if(i!=j) scanf("%lld",&a[i][j]);
//	for(int i=1;i<=n;i++)
//	{
//		for(int j=1;j<=n;j++)
//			printf("%lld ",a[i][j]);
//		printf("\n");
//	}
	for(int i=1;i<=n+1;i++)
		for(int j=1;j<=n+1;j++)
		{
			s1[i][j]=s1[i-1][j]+s1[i][j-1]-s1[i-1][j-1];
			if(i>j) s1[i][j]+=a[i][j];
			s2[i][j]=s2[i-1][j]+s2[i][j-1]-s2[i-1][j-1];
			if(i<j) s2[i][j]+=a[i][j];
		}
//	for(int i=1;i<=n+1;i++)
//	{
//		for(int j=1;j<=n+1;j++)
//			printf("%lld ",s1[i][j]);
//		printf("\n");
//	}
	memset(f,63,sizeof(f));
	f[0][0]=0;
	for(int i=0;i<=n;i++)
		for(int j=i;j<=n;j++)
			if(f[i][j]<INF)
				for(int k=j+1;k<=n+1;k++)

					{
						long long t=calc1(i+1,j,k+1,n+1)+calc2(j+1,k,j+1,k);
						f[j][k]=min(f[j][k],f[i][j]+t);
//						cerr<<"f"<<i<<" "<<j<<" "<<f[i][j]<<" ccc"<<" "<<t<<" "<<"to "<<j<<" "<<k<<" "<<f[j][k]<<"\n";
					}
	long long res=INF;
	for(int i=0;i<=n;i++)
		res=min(res,f[i][n+1]);
	printf("%lld",res);
	return 0;
}
