Good old Berland has n cities and m roads. Each road connects a pair of distinct cities and is bidirectional. Between any pair of cities, there is at most one road. For each road, we know its length.

We also know that the President will soon ride along the Berland roads from city s to city t. Naturally, he will choose one of the shortest paths from s to t, but nobody can say for sure which path he will choose.

The Minister for Transport is really afraid that the President might get upset by the state of the roads in the country. That is the reason he is planning to repair the roads in the possible President's path.

Making the budget for such an event is not an easy task. For all possible distinct pairs s, t (s < t) find the number of roads that lie on at least one shortest path from s to t.

Input

The first line of the input contains integers n, m (2 ≤ n ≤ 500, 0 ≤ m ≤ n·(n - 1) / 2) — the number of cities and roads, correspondingly. Then m lines follow, containing the road descriptions, one description per line. Each description contains three integers x_i, y_i, l_i (1 ≤ x_i, y_i ≤ n, x_i ≠ y_i, 1 ≤ l_i ≤ 10⁶), where x_i, y_i are the numbers of the cities connected by the i-th road and l_i is its length.

Output

Print the sequence of $\text{[math]}$ integers c₁₂, c₁₃, ..., c_1n, c₂₃, c₂₄, ..., c_2n, ..., c_{n - 1, n}, where c_st is the number of roads that can lie on the shortest path from s to t. Print the elements of sequence c in the described order. If the pair of cities s and t don't have a path between them, then c_st = 0.

Idx	Name	Rating
A	Guess a number!	1400
B	Art Union	1300
C	Booking System	1600
D	Population Size	2400
E	President's Path	2500

Codeforces Round 241 (Div. 2)