Description

After graduation, Drahc joined YiHoMo and became a game designer. He has finished an outline of a map for his new game. There are several places on his map.

However, his boss, Teafrogsf, has proposed several suggestions that require Drahc to modify the map. After days and nights of revisions, Drahc fainted. But there still exists a last requirement for the map. You decide to assist him.

For convenience, we use a positive weighted undirected graph $G=(V,E)$ to represent the map. This requirement requires that for all spanning subgraphs of $G$, there exists a unique spanning subgraph that has a minimum sum of weight. In other words, $\exists !G' = (V,E')$ s.t. $\sum_{e\in G'}w(e)$ minimizes ($E'\subset E$).

Drahc's map is under protection, so you can only modify one edge $e\in E$ at one time with its weight increased by $1$. Drahc wants his map to be modified as little as possible. Therefore, you need to modify as few times as possible, and since the modification method may not be unique, you only need to output the minimum number of modifications.

Format

Input

The first line of input contains $2$ integers: $n,m\,(1\leq n\leq 10^5, 1\leq m\leq 2\times10^5)$. $n$ represents the number of vertices in $G$ and $m$ represents the number of edges in $G$.

The next $m$ lines, each containing $3$ integers each: $u_i,v_i$ and $w_i\,(1\leq u_i,v_i\leq n, 1\leq w_i\leq 10^9)$. It means there exists an edge between $u_i$ and $v_i$ which is weighted $w_i$.

Output

One integer: the minimum number of modifications.

Samples

6 8
1 2 1
1 3 1
2 3 1
4 5 1
4 6 1
5 6 2
1 4 2
3 5 2

2