Constraints

* 1 ≤ |V| ≤ 100
* 0 ≤ |E| ≤ 9900
* -2 × 107 ≤ di ≤ 2 × 107
* There are no parallel edges
* There are no self-loops

Input

An edge-weighted graph G (V, E).


|V| |E|
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1


|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively.

si and ti represent source and target vertices of i-th edge (directed) and di represents the cost of the i-th edge.

Output

If the graph contains a negative cycle (a cycle whose sum of edge costs is a negative value), print


NEGATIVE CYCLE


in a line.

Otherwise, print


D0,0 D0,1 ... D0,|V|-1
D1,0 D1,1 ... D1,|V|-1
:
D|V|-1,0 D1,1 ... D|V|-1,|V|-1


The output consists of |V| lines. For each ith line, print the cost of the shortest path from vertex i to each vertex j (j = 0, 1, ... |V|-1) respectively. If there is no path from vertex i to vertex j, print "INF". Print a space between the costs.

Examples

Input

4 6
0 1 1
0 2 5
1 2 2
1 3 4
2 3 1
3 2 7


Output

0 1 3 4
INF 0 2 3
INF INF 0 1
INF INF 7 0


Input

4 6
0 1 1
0 2 -5
1 2 2
1 3 4
2 3 1
3 2 7


Output

0 1 -5 -4
INF 0 2 3
INF INF 0 1
INF INF 7 0


Input

4 6
0 1 1
0 2 5
1 2 2
1 3 4
2 3 1
3 2 -7


Output

NEGATIVE CYCLE
#include<bits/stdc++.h>
#define mx 2000000000
using namespace std;
int main(void)
{
	int v,e;
	int a,b,c,d[101][101],i,j,k;
	
	cin>>v>>e;
	
	for(i=0;i<v;i++){
		for(j=0;j<v;j++){
			if(i==j) d[i][j]=0;
			else d[i][j]=mx;
		}
	}
	
	for(i=0;i<e;i++){
		cin>>a>>b>>c;
		d[a][b]=c;
	}	
		
	for(k=0;k<v;k++){
		for(i=0;i<v;i++){
			for(j=0;j<v;j++){
				if(d[i][k]==mx||d[k][j]==mx) continue;
				else d[i][j]=min(d[i][j],d[i][k]+d[k][j]);
			}
		}
	}
	
	int flg=0;
	for(i=0;i<v;i++){
		for(j=0;j<v;j++){
			if(i==j&&d[i][j]<0) flg=1;
		}
	}
	
	if(flg==1) cout<<"NEGATIVE CYCLE"<<endl;
	
	if(flg==0){
		for(i=0;i<v;i++){
			for(j=0;j<v;j++){
				if(mx==d[i][j]&&j==0) cout<<"INF";
				else if(mx!=d[i][j]&&j==0) cout<<d[i][j];
				else if(mx==d[i][j]&&j!=0) cout<<" "<<"INF";
				else cout<<" "<<d[i][j];
			}
			cout<<endl;
		}	
	}
	
	return 0;
}	
