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 Python3 (judge verdict: Accepted)

import sys

def warshall_floyd(v_count: int, matrix: list) -> list:
    """ ワーシャルフロイド
    :param v_count: 頂点数
    :param matrix: 隣接行列
    """
    for i in range(v_count):
        for j, c2 in ((j, matrix[j][i]) for j in range(v_count)):
            for k, (c1, c3) in enumerate(zip(matrix[j], matrix[i])):
                if c1 > c2+c3:
                    matrix[j][k] = c2+c3
    return matrix


def has_negative_cycle(matrix: list) -> bool:
    """ 負閉路チェック
    :param matrix: 隣接行列(ワーシャルフロイドの結果)
    """
    return any(row[i] < 0 for i, row in enumerate(matrix))


V, E = map(int, input().split())
inf = float("inf")
matrix = [[inf]*V for _ in [0]*V]
for i in range(V):
    matrix[i][i] = 0
for s, t, d in (map(int, l.split()) for l in sys.stdin):
    matrix[s][t] = d
warshall_floyd(V, matrix)
if has_negative_cycle(matrix):
    print("NEGATIVE CYCLE")
else:
    for row in matrix:
        print(" ".join(map(lambda n: str(n) if n!=inf else "INF", row)))