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;
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define rrep(i,a,b) for(int i=(a);i>=(b);--i)
#define MP make_pair
#define PB push_back
typedef long long LL;
typedef unsigned long long ULL;
const LL MOD = 998244353;
const int N = 505;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

int n,x,a[N][N];
LL s1[N][N], s2[N][N], dp[N][N];

int main(){
	//freopen("test.in","r",stdin);
	scanf("%d",&n);
	rep(i,1,n)rep(j,1,n-1){
		scanf("%d",&x);
		a[i][j+(j>=i)]=x;
	}
	
	rep(i,1,n){
		LL sum1 = 0, sum2 = 0;
		rep(j,i,n){
			sum1 += a[i][j], sum2 += a[j][i];
			s1[i][j] = s1[i-1][j] + sum1;
			s2[i][j] = s2[i-1][j] + sum2;
			//cout<<i<<" "<<j<<" "<<s1[i][j]<<" "<<s2[i][j]<<endl;
		} 
	}
	
	rep(i,0,n+1)rep(j,0,n+1)dp[i][j]=1e18;
	rep(i,2,n)dp[i][1] = s1[i-1][i-1];
	rep(i,2,n)rep(j,1,i-1)rep(x,i+1,n){
		LL sum1 = s1[x-1][x-1] - s1[i-1][x-1];
		LL sum2 = s2[i-1][n] - s2[j-1][n] - s2[i-1][x-1] + s2[j-1][x-1];
		dp[x][i] = min(dp[x][i], dp[i][j] + sum1 + sum2);
		//cout<<x<<" "<<i<<" "<<j<<" "<<dp[x][i]<<endl;//<<sum1<<" "<<sum2<<endl;
	}
	LL ans = s1[n][n];
	rep(i,2,n)rep(j,1,i-1) ans = min(ans, dp[i][j]+s1[n][n]-s1[i-1][n]);
	printf("%lld\n",ans);
	return 0;
}