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
import java.util.Arrays;
import java.util.Scanner;

// ???????????£??????????????? wf
public class Main {
    static final int INF = Integer.MAX_VALUE;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int en = sc.nextInt();

        // wf ?????????
        int[][] d = new int[n][n];
        for (int i = 0; i < n; i++) {
            Arrays.fill(d[i], INF);
            d[i][i] = 0;
        }
        for (int i = 0; i < en; i++) {
            int s = sc.nextInt();
            int t = sc.nextInt();
            int dist = sc.nextInt();
            d[s][t] = dist;
            // ????????°??????
            // d[t][s] = dist;
        }

        // wf ??????
        for (int k = 0; k < n; k++) {
            for (int i = 0; i < n; i++) {
                if (d[i][k] == INF) {
                    continue;
                }
                for (int j = 0; j < n; j++) {
                    if (d[k][j] == INF) {
                        continue;
                    }
                    d[i][j] = Math.min(d[i][j], d[i][k] + d[k][j]);
                }
            }
        }

        // negative loop check
        if (hasNegativeLoopWF(d)) {
            System.out.println("NEGATIVE CYCLE");
            return;
        }
        for (int i = 0; i < n; i++) {
            String[] res = new String[n];
            for (int j = 0; j < n; j++) {
                res[j] = d[i][j] == INF ? "INF" : String.valueOf(d[i][j]);
            }
            System.out.println(String.join(" ", res));
        }
    }

    public static boolean hasNegativeLoopWF(int[][] a) {
        for (int i = 0; i < a.length; i++) {
            if (a[i][i] < 0) {
                return true;
            }
        }
        return false;
    }
}