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;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef long long LL;
typedef vector<LL> VL;
typedef vector<VL> VVL;
typedef pair<int,int> PI; 
typedef pair<LL,LL> PLL;
typedef unsigned long long ULL;
typedef pair<double,double> PD;

#define FOR(x, b, e) for(int x = b; x<= (e); x++)
#define FORD(x, b, e) for(int x = b; x>= (e); x--)
#define REP(x, n) for(int x = 0; x<(n); ++x)
#define ALL(c) (c).begin(), (c).end()
#define SIZE(x) ((int)(x).size())

#define PB push_back
#define IN insert
#define ST first
#define ND second
#define INF 2000000011
#define MOD 1000000007

#define MAXS 510

int n;

int main(){
	
	ios::sync_with_stdio(0); cin.tie(0);
	cin>>n;
	
	VVL dp(n,VL(n,LONG_LONG_MAX));
	VVL pref(n,VL(n));
	VVI tab(n,VI(n));
	
	FOR(i,0,n-1){
		FOR(j,0,n-1){
			if(i==j)
				continue;
			cin>>tab[i][j];
		}
	}
	
	FOR(dl,1,n){
		REP(i,n){
			int j=dl+i;
			if(j>=n)
				break;
			if(dl==1){
				pref[i][j]=tab[i][j];
				pref[j][i]=tab[j][i];
			}
			else{
				pref[i][j]=pref[i][j-1]+pref[i+1][j]-pref[i+1][j-1]+tab[i][j];
				pref[j][i]=pref[j-1][i]+pref[j][i+1]-pref[j-1][i+1]+tab[j][i];
			}
		}
	}
	
	REP(i,n){
		if(i==0){
			FOR(j,0,n-1)
				dp[0][j]=min(dp[0][j],pref[0][j]);
		}
		else{
			FOR(j,i,n-1)
				REP(k,i)
					dp[i][j]=min(dp[i][j],dp[k][i-1]+pref[i][j]+pref[j][0]-pref[j][k]-pref[i-1][0]+pref[i-1][k]);
		}
	}
	
	LL wyn=LONG_LONG_MAX;
	REP(i,n)
		wyn=min(wyn,dp[i][n-1]);
	cout<<wyn;
	
	return 0;
}
