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;
const int N=500+5;
long long n,a[N][N],g[2][N][N],f[N][N],cnt,sum=0x3f3f3f3f3f3f3f3f;
void init(){
	scanf("%lld",&n);
	for(int i=0;++i<=n;) for(int j=0;++j<=n;i==j?:scanf("%lld",&a[i][j]));
}
long long gg(int k,int lx,int ly,int rx,int ry){
	return g[k][rx][ry]-g[k][lx-1][ry]-g[k][rx][ly-1]+g[k][lx-1][ly-1];
}
void work(){
	for(int i=0;++i<=n;){
		for(int j=0;++j<=n;i>=j?:g[0][i][j]=a[i][j],g[0][i][j]+=g[0][i][j-1]);
		for(int j=0;++j<=n;g[0][i][j]+=g[0][i-1][j]);
	}
	for(int i=0;++i<=n;){
		for(int j=0;++j<=n;i<=j?:g[1][i][j]=a[i][j],g[1][i][j]+=g[1][i][j-1]);
		for(int j=0;++j<=n;g[1][i][j]+=g[1][i-1][j]);
	}
	memset(f,0x3f,sizeof(f));
	f[0][0]=0;
	for(int i=-1;++i<=n;) for(int j=-1;++j<max(i,1);) for(int h=i;++h<=n;
		cnt=f[i][j]+gg(1,h+1,j+1,n,i)+gg(0,i+1,i+1,h,h),f[h][i]=min(f[h][i],cnt));
	for(int i=0;++i<=n;sum=min(sum,f[n][i]));
}
void prin(){
	printf("%lld",sum);
}
int main(){
	init();
	work();
	prin();
	return 0;
}