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
//by yjz
#include<bits/stdc++.h>
#define FF first
#define SS second
#define MP make_pair
#define PB push_back
typedef long long ll;
using namespace std;
const int maxn = 511;
ll inf;
int n;
int a[maxn][maxn];
ll dp[maxn][maxn], ca[maxn][maxn], cb[maxn][maxn];
ll suma[maxn][maxn], sumb[maxn][maxn];
void upd(ll &x, ll v) {x=min(x, v);}
int main()
{
	scanf("%d", &n);
	for (int i=1; i<=n; i++)
	{
		for (int j=1; j<=n; j++)
		{
			if (i!=j) scanf("%d", &a[i][j]);
		}
	}
	for (int i=1; i<=n; i++)
	{
		ll sum = 0;
		for (int j=i; j>=0; j--)
		{
			ca[i][j] = sum;
			sum += a[j][i];
		}
	}
	for (int i=1; i<=n; i++)
	{
		ll sum = 0;
		for (int j=1; j<=i; j++)
		{
			cb[i][j] = sum;
			sum += a[i][j];
		}
	}
	for (int i=0; i<=n; i++)
	{
		for (int j=0; j<=n; j++)
		{
			suma[i][j] = ca[i][j];
			sumb[i][j] = cb[i][j];
		}
	}
	for (int i=1; i<=n+1; i++) for (int j=0; j<=n+1; j++)
	{
		suma[i][j] += suma[i-1][j];
		sumb[i][j] += sumb[i-1][j];
	}
	memset(dp, 20, sizeof(dp));
	inf = dp[0][0];
	dp[n+1][n+1] = 0;
	for (int i=n+1; i>=1; i--)
	{
		for (int j=i; j<=n+1; j++)
		{
			ll &cur = dp[i][j];
			if (cur>=inf) continue;
			for (int k=0; k<i; k++)
			{
				ll c = 0;
				c += suma[j][i-1]-suma[i-1][i-1];
				c += sumb[j][k]-sumb[i-1][k];
				upd(dp[k][i-1], dp[i][j]+c);
			}
		}
	}
	cout<<dp[0][0]<<endl;
	return 0;
}