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;

#define Inf ll(1e18)
#define rep(i,n) for(int i=0;i<(n);i++)
#define REP(i,n) for(int i=1;i<=(n);i++)
#define mp make_pair
#define pb push_back
#define fst first
#define snd second
typedef long long ll;
typedef pair<int,int> pii;

const int maxn=505;
int n;
ll a[maxn][maxn],sum[2][maxn][maxn],dp[maxn][maxn],ans;
void ckmax(ll &a,ll b){
	if(b>a)a=b;
}
ll getval(int tp,int x1,int x2,int y1,int y2){
	if(x1>x2||y1>y2)return 0;
	return sum[tp][x2][y2]+sum[tp][x1-1][y1-1]-sum[tp][x2][y1-1]-sum[tp][x1-1][y2];
}

int main(){
	scanf("%d",&n);
	REP(i,n)REP(j,n){
		if(i==j)a[i][j]=0;
		else{
			scanf("%lld",&a[i][j]);
			if(i>j)sum[0][i][j]=a[i][j];
			else sum[1][j][i]=a[i][j];
		}
	}
	REP(i,n)REP(j,n)sum[0][i][j]+=sum[0][i][j-1],sum[1][i][j]+=sum[1][i][j-1];
	REP(i,n)REP(j,n)sum[0][i][j]+=sum[0][i-1][j],sum[1][i][j]+=sum[1][i-1][j];
	REP(i,n)REP(j,n)dp[i][j]=-Inf;
	dp[1][1]=0;
	REP(i,n)REP(j,n)if(dp[i][j]!=-Inf){
		ckmax(ans,dp[i][j]+getval(0,j+1,n,i,n)+getval(1,j+1,n,1,j-1));
		for(int k=j+1;k<=n;k++){
			if(k==1)continue;
			ll cur1=getval(0,k,k,j,k-1)+getval(0,j+1,k-1,i,k-1);
			ll cur2=getval(1,k,k,1,k-1)+getval(1,j+1,k-1,1,j-1);
			ckmax(dp[j][k],dp[i][j]+cur1+cur2);
		}
	}
	printf("%lld\n",sum[0][n][n]+sum[1][n][n]-ans);
	return 0;
} 