removeedges

Shiwei city is a connected undirected graph with N cities and M roads, with cities numbered 1 to N and roads numbered from 1 to M. City i has a value of X_i and edge i has a values of Y_i connecting node A_i and B_i.

Zane the (redacted) wants to remove some edges to make Shiwei happy. Specifically, Shiwei hopes that for each roads not removed, the sum of the values of the cities in the connected component containing that road is greater than or equal to the value of that roads.

Zane is lazy. Find the minimum number of edges that need to be removed.

Constraints

Input Format

First line of input contains 2 integers N and M

Next line contains N integers representing X

Next M lines contain 3 integers, A_i, B_i, Y_i

Output Format

Output the minimum number of roads Zane needs to destroy

Sample