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>

using namespace std;

using ll = long long;
constexpr ll MOD = 1e9 + 7;
constexpr ll INF = 1e18;

int main() {
    ll V,E;
    cin >> V >> E;
    vector<vector<ll>> G(V,vector<ll>(V,INF));
    for(ll i=0;i<E;i++){
        ll x,y,cost;
        cin >> x >> y >> cost;
        G[x][y] = cost;
    }
    for(ll i=0;i<V;i++)G[i][i] = 0;
    for(ll k=0;k<V;k++){
        for(ll i=0;i<V;i++){
            for(ll j=0;j<V;j++){
                if(G[i][k]!=INF && G[k][j]!=INF)G[i][j] = min(G[i][j],G[i][k]+G[k][j]);
            }
        }
    }
    for(ll i=0;i<V;i++){
        if(G[i][i]<0){
            cout << "NEGATIVE CYCLE" << endl;
            return 0;
        }
    }
    for(ll i=0;i<V;i++){
        for(ll j=0;j<V;j++){
            if(G[i][j]==INF){
                cout << "INF";
            }else {
                cout << G[i][j];
            }
            cout << (j==V-1 ? '\n':' ');
        }
    }
}
