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>
#define gmi(a,b) a=(a)<(b)?(a):(b)
#define FOR(i,a,b) for(int i=a;i<=b;i++)
#define FOF(i,a,b) for(int i=a;i< b;i++)
using namespace std;
typedef long long ll;
const int N=550;
const ll INF=1e18;
int n,x;
ll ans,a[N][N],b[N][N],f[N][N];
ll SB(int x,int y){return b[x][x]-b[x][y]-b[y][x]+b[y][y];}
int main(){
	//freopen("1.in","r",stdin);
	scanf("%d",&n);
	FOF(i,0,n)FOF(j,0,n)if(i!=j){
		scanf("%d",&x);
		j<i?a[j+1][i]=x:b[i+1][j]=x;
	}
	FOR(i,1,n)FOR(j,1,n){
		a[i][j]+=a[i-1][j]+a[i][j-1]-a[i-1][j-1];
		b[i][j]+=b[i-1][j]+b[i][j-1]-b[i-1][j-1];
	}
	FOR(i,1,n)FOR(j,0,i) f[i][j]=INF;
	FOR(i,1,n)FOR(j,0,i)FOR(k,0,j)
		gmi(f[i][j],f[j][k]+a[k][i-1]-a[k][j-1]+SB(i-1,j));
	//FOR(i,1,n)FOR(j,0,i-1) cout<<f[i][j]<<" \n"[j==i-1];
	ans=INF;
	FOF(j,0,n) ans=min(ans,f[n][j]);
	cout<<ans<<'\n';
}