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<iostream>
#include<climits>

using namespace std;

const long long MAX=LLONG_MAX>>1;

int main(){
	int v=0,e=0;
	long long dist[100][100]={0};
	cin>>v>>e;
	for(int i=0;i<v;i++){
		for(int j=0;j<v;j++){
			dist[i][j]=MAX;
		}
	}
	for(int i=0;i<v;i++){
		dist[i][i]=0;
	}
	for(int i=0;i<e;i++){
		int s=0,t=0,d=0;
		cin>>s>>t>>d;
		dist[s][t]=d;
	}
	for(int i=0;i<v;i++){
		for(int j=0;j<v;j++){
			for(int k=0;k<v;k++){
				if(dist[j][k]>dist[j][i]+dist[i][k] && dist[j][i]!=MAX && dist[i][k]!=MAX){dist[j][k]=dist[j][i]+dist[i][k];}
			}
		}
	}
	for(int i=0;i<v;i++){
		if(dist[i][i]<0){
			cout<<"NEGATIVE CYCLE"<<endl;
			return 0;
		}
	}
	for(int i=0;i<v;i++){
		for(int j=0;j<v;j++){
			if(dist[i][j]==MAX){cout<<"INF";}
			else{cout<<dist[i][j];}
			cout<<(j==v-1?"\n":" ");
		}
	}
	return 0;
}