You are given a graph with ~N~ vertices and ~M~ edges. Each edge is a directed edge from vertex ~u_i~ to vertex ~v_i~ with weight ~w_i~. You are asked to find the shortest path between all pairs of vertices. The graph may contain multiple edges between any pair of vertices, as well as self-loops. There may also be negative edge weights. It is not guaranteed that the graph is connected.

Constraints

For all subtasks,

~0 \le M \le 4\,000~

~1 \le u_i, v_i \le N~

Subtask 1 [10%]

~1 \le N \le 300~

~-10^9 \le w_i \le 10^9~

Subtask 2 [10%]

~1 \le N \le 1\,000~

~1 \le w_i \le 10^9~

Subtask 3 [80%]

~1 \le N \le 1\,000~

~-10^9 \le w_i \le 10^9~

Input Specification

The first line contains 2 integers ~N~ and ~M~, subject to the constraints above.

The next ~M~ lines describe the edges of the graph. Each line contains 3 integers, ~u_i~, ~v_i~, ~w_i~, indicating a directed edge from vertex ~u_i~ to vertex ~v_i~ with weight ~w_i~, subject to the constraints above.

Output Specification

This problem is graded with an identical checker. This includes whitespace characters. Ensure that every line of output is terminated with a \n character.

The output consists of ~N~ lines, each with ~N~ space separated integers. Each line should end with a new line character. Integer ~j~ on line ~i~ contains the distance of the shortest path from vertex ~i~ to vertex ~j~.

If there is no path from ~i~ to ~j~, INF should be printed instead of an integer.

If there is no lower bound on the length of the shortest path from ~i~ to ~j~ (or equivalently, there is a path from ~i~ to ~j~ that contains a negative edge cycle), -INF should be printed instead of an integer.

A negative edge cycle is a path that starts and ends on the same vertex, and the sum of the weights of those edges on that path is less that ~0~.

Sample Input 1

5 4
1 2 9
1 4 8
2 4 2
3 5 4

Sample Output 1

0 9 INF 8 INF
INF 0 INF 2 INF
INF INF 0 INF 4
INF INF INF 0 INF
INF INF INF INF 0

Sample Input 2

6 6
1 2 2
1 3 4
2 3 -10
3 5 1
5 6 2
6 5 -5

Sample Output 2

0 2 -8 INF -INF -INF
INF 0 -10 INF -INF -INF
INF INF 0 INF -INF -INF
INF INF INF 0 INF INF
INF INF INF INF -INF -INF
INF INF INF INF -INF -INF