Problem:
All Pairs Shortest Path

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.

Constraints

1 ≤ |V| ≤ 100

0 ≤ |E| ≤ 9900

-2 × 107 ≤ di ≤ 2 × 107

There are no parallel edges

There are no self-loops

Sample Input 1

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

Sample Output 1

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

Sample Input 2

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

Sample Output 2

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

Sample Input 3

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

Sample Output 3

NEGATIVE CYCLE

Solution in JAVA (judge verdict: Wrong Answer)

import java.util.Scanner;

public class Main {
    static Scanner sc = new Scanner(System.in);
    static final int MAX_V = 105;
    static final int INF = 1 << 31 - 1;
    static int V, E;
    static long [][] dp = new long[MAX_V][MAX_V];

    public static void main(String[] args) {
        init();
        read();
        out();
        solve();
        out();
    }

    static void read() {
        V = sc.nextInt();
        E = sc.nextInt();
        int s, t, d;
        for (int i = 0; i < E; i++) {
            s = sc.nextInt();
            t = sc.nextInt();
            d = sc.nextInt();
            dp[s][t] = d;
        }
    }

    static void init() {
        for (int i = 0; i < MAX_V; i++) {
            for (int j = 0; j < MAX_V; j++) {
                if (i == j) {
                    dp[i][j] = 0;
                } else {
                    dp[i][j] = INF;
                }
            }
        }
    }

    static void solve() {
        for (int k = 0; k < V; k++) {
            for (int i = 0; i < V; i++) {
                for (int j = 0; j < V; j++) {
                    dp[i][j] = Math.min(dp[i][j], dp[i][k] + dp[k][j]);
                }
            }
        }
    }

    static void out() {
        String s = "";
        for (int i = 0; i < V; i++) {
            for (int j = 0; j < V; j++) {
                if (i == j && dp[i][j] < 0) {
                    System.out.println("NEGATIVE CYCLE");
                    return;
                }

                if (dp[i][j] == INF) {
                    s += "INF ";
                } else {
                    s += String.format("%d ", dp[i][j]);
                }
            }
            s = s.trim() + "\n";
        }
        System.out.print(s);
    }
}