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 <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <vector>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <queue>
#include <ctime>
#include <cassert>
#include <complex>
#include <string>
#include <cstring>
#include <chrono>
#include <random>
#include <queue>
#include <bitset>
using namespace std;

#ifdef LOCAL
	#define eprintf(...) fprintf(stderr, __VA_ARGS__)
#else
	#define eprintf(...) 42
#endif

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, int> pli;
typedef pair<ll, ll> pll;
typedef long double ld;
#define mp make_pair
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

const int N = 505;
const ll INF = (ll)1e18;
ll a[N][N];
ll b[N][N];
ll dp[N][N];
int n;

ll getSum(int l, int r, int x, int y) {
	return a[l][x] + a[r][y] - a[l][y] - a[r][x];
}
ll getCost(int i, int j, int k) {
	return getSum(k, n, i, j) + b[j][k];
}

int main()
{
//	freopen("input.txt", "r", stdin);
//	freopen("output.txt", "w", stdout);

	scanf("%d", &n);
	for (int i = 0; i < n; i++)
		for (int j = 0; j < n; j++) {
			if (i != j)
				scanf("%lld", &a[i + 1][j + 1]);
			a[i + 1][j + 1] += a[i + 1][j] + a[i][j + 1] - a[i][j];
		}
	for (int len = 1; len <= n; len++) {
		for (int l = 0; l + len <= n; l++) {
			int r = l + len;
			b[l][r] = b[l + 1][r] + getSum(l, l + 1, l, r);
		}
	}
	for (int i = 0; i < n; i++)
		for (int j = i; j <= n; j++)
			dp[i][j] = INF;
	for (int i = 1; i <= n; i++)
		dp[0][i] = b[0][i];
	for (int i = 0; i < n; i++)
		for (int j = i + 1; j < n; j++)
			for (int k = j + 1; k <= n; k++) {
				dp[j][k] = min(dp[j][k], dp[i][j] + getCost(i, j, k));
			}
	ll ans = INF;
	for (int i = 0; i < n; i++)
		ans = min(ans, dp[i][n]);
	printf("%lld\n", ans);

	return 0;
}
