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<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
using namespace std;
#define int long long
#define MAXN 506
int n;
int dp[MAXN][MAXN] , Sa[MAXN][MAXN] , Si[MAXN][MAXN];
int A[MAXN][MAXN] , B[MAXN][MAXN];
signed main() {
	cin >> n;
	for( int i = 1 ; i <= n ; ++ i ) {
		for( int j = 1 ; j < i ; ++ j ) 
			scanf("%lld",&A[j][i]);
		for( int j = i + 1 ; j <= n ; ++ j )
			scanf("%lld",&B[i][j]);
	}
	for( int i = 1 ; i <= n ; ++ i ) 
		for( int j = n ; j >= i + 1 ; -- j ) {
			Sa[i][j] = Sa[i][j + 1];
			for( int k = 1 ; k <= i ; ++ k ) Sa[i][j] += A[k][j];
		}
	for( int i = 1 ; i <= n ; ++ i ) 
		for( int j = i + 1 ; j <= n + 1 ; ++ j ) {
			Si[i][j] = Si[i][j - 1];
			for( int k = i ; k <= j - 1 ; ++ k ) Si[i][j] += B[k][j];
		}
	memset( dp , 0x3f3f , sizeof dp );
	dp[0][0] = 0;
	for( int i = 0 ; i <= n ; ++ i ) 
		for( int j = i ; j <= n ; ++ j )
			if( dp[i][j] < 0x3f3f3f3f3f3f3f3f ) {
				for( int k = j + 1 ; k <= n + 1 ; ++ k ) 
					dp[j][k] = min( dp[j][k] , dp[i][j] + Si[j + 1][k] + Sa[j][k + 1] - Sa[i][k + 1] );
			}
	int ans = 0x3f3f3f3f3f3f3f3f;
	for( int i = 0 ; i <= n ; ++ i ) 
		ans = min( ans , dp[i][n + 1] );
	cout << ans << endl;
}