Given a bidirectional, connected, weighted graph with ~N~ nodes and ~M~ edges, find the difference between the sum of the edges of the maximum and minimum spanning trees of the graph.

Constraints

~1 \le N, M \le 2 \times 10^5~

Input Specification

The first line of input will contain ~2~ space-separated integers ~N~ and ~M~.

The next ~M~ lines will contain ~3~ space-separated integers ~u~, ~v~, and ~w \ (1 \le u, v \le N, 1 \le w \le 10^9)~ denoting an edge.

Output Specification

Output one integer, the difference between the sum of the edges of the maximum and minimum spanning trees.

Note: 64-bit integers may be required for this problem.

Sample Input

4 5
1 2 1
1 3 2
2 3 5
2 4 4
3 4 3

Sample Output

5

The graph given is shown in the above figure. The sum of the edges of the minimum spanning tree is ~6~ using edges ~1~, ~2~, and ~5~ (in the sample input). The sum of the edges of the maximum spanning tree is ~11~, using edges ~2~, ~3~, and ~4~. The difference is thus ~5~.