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>
// iostream is too mainstream
#include <cstdio>
// bitch please
#include <iostream>
#include <algorithm>
#include <cstdlib>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <list>
#include <cmath>
#include <iomanip>
#include <time.h>
#define dibs reserve
#define OVER9000 1234567890
#define ALL_THE(CAKE,LIE) for(auto LIE =CAKE.begin(); LIE != CAKE.end(); LIE++)
#define tisic 47
#define soclose 1e-8
#define chocolate win
// so much chocolate
#define patkan 9
#define ff first
#define ss second
#define abs(x) (((x) < 0)?-(x):(x))
#define uint unsigned int
#define dbl long double
#define pi 3.14159265358979323846
using namespace std;
// mylittledoge

using cat = long long;

#ifdef DONLINE_JUDGE
	// palindromic tree is better than splay tree!
	#define lld I64d
#endif

int main() {
	cin.sync_with_stdio(0);
	cin.tie(0);
	cout << fixed << setprecision(10);
	int N;
	cin >> N;
	vector< vector<cat> > A_sum_pos(N, vector<cat>(N+1, 0));
	vector< vector<cat> > A_sum_neg(N, vector<cat>(N+1, 0));
	for(int i = 0; i < N; i++) {
		for(int j = 0; j < i; j++) cin >> A_sum_pos[i][j];
		for(int j = i+1; j < N; j++) cin >> A_sum_neg[j][i];
	}
	for(int i = 0; i < N; i++) {
		for(int j = 0; j < N; j++) A_sum_neg[i][j+1] += A_sum_neg[i][j];
		for(int j = i-1; j >= 0; j--) A_sum_pos[i][j] += A_sum_pos[i][j+1];
	}
	vector< vector<cat> > sum(N, vector<cat>(N, 0));
	for(int i = 1; i < N; i++) sum[i][0] = sum[i-1][0] + A_sum_pos[i][0];
	for(int i = 0; i < N; i++) for(int j = 0; j <= i; j++) {
		cat sp = 0, sn = 0;
		for(int k = i+1; k < N; k++) {
			sp += A_sum_pos[k][j];
			sn += A_sum_neg[k][i];
			sum[k][i+1] = max(sum[k][i+1], sum[i][j] + sp + sn);
		}
	}
	cat max_sum = 0;
	for(int i = 0; i < N; i++) max_sum = max(max_sum, sum[N-1][i]);
	cat ans = -max_sum;
	for(int i = 0; i < N; i++) ans += A_sum_pos[i][0] + A_sum_neg[i][N];
	cout << ans << "\n";
	return 0;
}

// look at my code
// my code is amazing
