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
nv, ne = map(int, input().split())

costs = [[None] * nv for _ in range(nv)]
for i in range(nv):
    costs[i][i] = 0

while ne:
    s, t, d = map(int, input().split())
    costs[s][t] = d
    ne -= 1


def loop():
    for k in range(nv):
        for i in range(nv):
            for j in range(nv):
                if costs[i][k] is None or costs[k][j] is None:
                    continue
                tmp_cost = costs[i][k] + costs[k][j]
                if i == j and tmp_cost < 0:
                    print('NEGATIVE CYCLE')
                    return False
                if costs[i][j] is None or costs[i][j] > tmp_cost:
                    costs[i][j] = tmp_cost
    return True


if loop():
    for vc in costs:
        print(*('INF' if c is None else c for c in vc))