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>
#define LL long long
#define fr(i,x,y) for(int i=(x);i<=(y);i++)
#define rf(i,x,y) for(int i=(x);i>=(y);i--)
#define frl(i,x,y) for(int i=(x);i<(y);i++)
using namespace std;
const int N=505;
const int p=998244353;
int n;
int a[N][N];
LL w[N][N],vv[N][N];
LL f[N][N];

void read(int &x){ scanf("%d",&x); }
void read(LL &x){ scanf("%lld",&x); }

LL vwv(int a,int b,int c){
	return w[b][c]-w[a-1][c];
}

void chkmin(LL &x,LL y){
	if (y<x) x=y;
}

int main(){
	read(n);
	fr(i,1,n)
	 fr(j,1,n)
	  if (i!=j) read(a[i][j]);
	fr(i,1,n)
	 rf(j,n,i+1){
	 	w[i][j]=w[i][j+1];
	 	fr(k,1,i) w[i][j]+=a[j][k];
	 }
	fr(i,1,n)
	 fr(j,i+1,n+1){
	 	vv[i][j]=vv[i][j-1];
	 	fr(k,i,j-1) vv[i][j]+=a[k][j];
	 }
	memset(f,0x3f,sizeof f);
	f[0][0]=0;
	fr(i,0,n)
	 fr(j,i,n)
	  if (f[i][j]<1e18){
	  	fr(k,j+1,n+1)
	  	 chkmin(f[j][k],f[i][j]+vv[j+1][k]+vwv(i+1,j,k+1));
	  }
	LL ans=1e18;
	fr(i,0,n) chkmin(ans,f[i][n+1]);
	cout<<ans<<endl;
	return 0;
}