All Pairs Shortest Path

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

inputFormat

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.

outputFormat

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

样例

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

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

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