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;
template <typename T> void read(T &t) {
	t=0; char ch=getchar(); int f=1;
	while (ch<'0'||ch>'9') { if (ch=='-') f=-1; ch=getchar(); }
	do { (t*=10)+=ch-'0'; ch=getchar(); } while ('0'<=ch&&ch<='9'); t*=f;
}
typedef long long ll;
const ll INF=1LL<<50;
int n;
ll ans,a[510][510],dp[510][510],s[2][510][510];
void update(ll &x,ll y) {
	if (x>y) x=y;
}
ll S(int k,int x1,int x2,int y1,int y2) {
	return s[k][x2][y2]-s[k][x1-1][y2]-s[k][x2][y1-1]+s[k][x1-1][y1-1];
}
int main() {
	//freopen("1.txt","r",stdin);
	read(n);
	for (int i=1;i<=n;i++)
	for (int j=1;j<=n;j++)
		if (i!=j) read(a[i][j]);
	for (int i=1;i<=n;i++)
	for (int j=1;j<=n;j++) {
		for (int k=0;k<2;k++) {
			s[k][i][j]=s[k][i-1][j]+s[k][i][j-1]-s[k][i-1][j-1];
		}
		s[i>j][i][j]+=a[i][j];
	}
	for (int i=0;i<=n;i++)
	for (int j=0;j<=n;j++) dp[i][j]=INF;
	dp[0][0]=0;
	for (int i=0;i<n;i++)
	for (int j=0;j<=i;j++) {
		if (dp[i][j]==INF) continue;
		//printf("%d %d %lld\n",i,j,dp[i][j]);
		for (int x=i+1;x<=n;x++)
			update(dp[x][i],dp[i][j]+S(0,i+1,x,i+1,x)+S(1,x+1,n,j+1,i));
	}
	ans=INF;
	for (int i=1;i<=n;i++) update(ans,dp[n][i]);
	printf("%lld\n",ans);
	return 0;
}
/*
  0. Enough array size? Enough array size? Enough array size? Interger overflow?
  
  1. Think TWICE, Code ONCE!
  Are there any counterexamples to your algo?
    
  2. Be careful about the BOUNDARIES!
  N=1? P=1? Something about 0?
    
  3. Do not make STUPID MISTAKES!
  Time complexity? Memory usage? Precision error?
*/