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<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long hxtype;
template<class IT>inline void cmax(IT &a,IT b){if(a<b)a=b;}
template<class IT>inline void cmin(IT &a,IT b){if(b<a)a=b;}
const int N=505;
ll a[N][N],s1[N][N],s2[N][N],dp[N][N];
inline ll get(int a,int b,int c){return s2[c][a]-s2[b-1][a]-s1[b][c];}
int main(){
	int n,i,j,k;ll sum=0ll,w;
	scanf("%d",&n);
	for(i=1;i<=n;++i){
		for(j=  1;j!=i;++j){scanf("%lld",&a[i][j]);sum+=a[i][j];}
		for(j=i+1;j<=n;++j){scanf("%lld",&a[i][j]);sum+=a[i][j];}
	}
	for(i=n;i   ;--i)for(j=i;j<=n;++j)s1[i][j]=s1[i+1][j]+s1[i][j-1]-s1[i+1][j-1]+a[i][j];
	for(i=1;i<=n;++i)for(j=n;j   ;--j)s2[i][j]=s2[i-1][j]+s2[i][j+1]-s2[i-1][j+1]+a[i][j];
	for(i=1;i<=n;++i)dp[1][i]=get(1,1,i);
	for(i=2;i<=n;++i)for(j=i;j<=n;++j){
		w=0ll;
//		for(k=1;k!=i;++k)printf("dp[%d][%d] %lld+%lld => dp[%d][%d]\n",k,i-1,dp[k][i-1],get(k,i,j),i,j);
		for(k=1;k!=i;++k)cmax(w,dp[k][i-1]+get(k,i,j));
		dp[i][j]=w;
	}
//	printf("S1\n");
//	for(i=1;i<=n;++i){for(j=1;j<=n;++j)printf("%lld ",s1[i][j]);printf("\n");}
//	printf("S2\n");
//	for(i=1;i<=n;++i){for(j=1;j<=n;++j)printf("%lld ",s2[i][j]);printf("\n");}
//	printf("DP\n");
//	for(i=1;i<=n;++i){for(j=1;j<=n;++j)printf("%lld ",dp[i][j]);printf("\n");}
	w=0ll;
	for(i=1;i<=n;++i)cmax(w,dp[i][n]);
	printf("%lld",sum-w);
	return 0;
}