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 ll long long
#define REP(i,a,b) for(int i=(a),_end_=(b);i<=_end_;i++)
#define DREP(i,a,b) for(int i=(a),_end_=(b);i>=_end_;i--)
#define EREP(i,u) for(int i=start[u];i;i=e[i].next)
#define fi first
#define se second
#define mkr(a,b) make_pair(a,b)
#define SZ(A) ((int)A.size())
template<class T>inline void chkmin(T &a,T b){ if(a>b)a=b;}
template<class T>inline void chkmax(T &a,T b){ if(a<b)a=b;}
inline int read()
{
	int s=0,f=1;char ch=getchar();
	while(!isdigit(ch) && ch!='-')ch=getchar();
	if(ch=='-')ch=getchar(),f=-1;
	while(isdigit(ch))s=s*10+ch-'0',ch=getchar();
	return ~f?s:-s;
}

const int maxn=520;
const ll inf=0x3f3f3f3f3f3f3f3f;

int n;
ll A[maxn][maxn];
ll B[maxn][maxn];

inline void init()
{
	n=read();
	REP(i,1,n)REP(j,1,n)
		if(i<j)A[i][j]=read();
		else if(i>j)B[j][i]=read();
	REP(i,1,n)REP(j,1,n)A[i][j]+=A[i-1][j];
	REP(i,1,n)REP(j,1,n)A[i][j]+=A[i][j-1];
	REP(i,1,n)REP(j,1,n)B[i][j]+=B[i-1][j];
	REP(i,1,n)REP(j,1,n)B[i][j]+=B[i][j-1];
	
}

ll f[maxn][maxn];

inline ll matrixA(int x1,int x2,int y1,int y2)
{
	if(x1>x2 || y1>y2)return 0;
	return A[x2][y2]-A[x1-1][y2]-A[x2][y1-1]+A[x1-1][y1-1];
}

inline ll matrixB(int x1,int x2,int y1,int y2)
{
	if(x1>x2 || y1>y2)return 0;
	return B[x2][y2]-B[x1-1][y2]-B[x2][y1-1]+B[x1-1][y1-1];
}

inline void doing()
{
	memset(f,inf,sizeof(f));
	f[0][0]=0;
	REP(i,0,n-1)REP(j,0,i)if(f[i][j]!=inf)
	{
		REP(k,i+1,n-1)
		{
			chkmin(f[k][i],f[i][j]+matrixA(i+1,k-1,i+1,k)+matrixB(1,j,i+1,k));
		}
	}
	ll ans=inf;
	REP(i,0,n-1)REP(j,0,i)if(f[i][j]!=inf)
	{
		chkmin(ans,f[i][j]+matrixA(i+1,n,i+1,n)+matrixB(1,j,i+1,n));
	}
	printf("%lld\n",ans);
}

int main()
{
	init();
	doing();
	return 0;
}
