Weights on Vertices and Edges

There is a connected undirected graph with N vertices and M edges. The vertices are numbered 1 to N, and the edges are numbered 1 to M. Also, each of these vertices and edges has a specified weight. Vertex i has a weight of X_i; Edge i has a weight of Y_i and connects Vertex A_i and B_i.

We would like to remove zero or more edges so that the following condition is satisfied:

• For each edge that is not removed, the sum of the weights of the vertices in the connected component containing that edge, is greater than or equal to the weight of that edge.

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

Constraints

• 1 \leq N \leq 10^5
• N-1 \leq M \leq 10^5
• 1 \leq X_i \leq 10^9
• 1 \leq A_i < B_i \leq N
• 1 \leq Y_i \leq 10^9
• (A_i,B_i) \neq (A_j,B_j) (i \neq j)
• The given graph is connected.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M X_1 X_2 ... X_N A_1 B_1 Y_1 A_2 B_2 Y_2 : A_M B_M Y_M

Output

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

Examples

Input

4 4 2 3 5 7 1 2 7 1 3 9 2 3 12 3 4 18

Output

2

Input

6 10 4 4 1 1 1 7 3 5 19 2 5 20 4 5 8 1 6 16 2 3 9 3 6 16 3 4 1 2 6 20 2 4 19 1 2 9

Output

4

Input

10 9 81 16 73 7 2 61 86 38 90 28 6 8 725 3 10 12 1 4 558 4 9 615 5 6 942 8 9 918 2 7 720 4 7 292 7 10 414

Output

8

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N M X_1 X_2 ... X_N A_1 B_1 Y_1 A_2 B_2 Y_2 : A_M B_M Y_M

outputFormat

Output

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

Examples

Input

4 4 2 3 5 7 1 2 7 1 3 9 2 3 12 3 4 18

Output

2

Input

6 10 4 4 1 1 1 7 3 5 19 2 5 20 4 5 8 1 6 16 2 3 9 3 6 16 3 4 1 2 6 20 2 4 19 1 2 9

Output

4

Input

10 9 81 16 73 7 2 61 86 38 90 28 6 8 725 3 10 12 1 4 558 4 9 615 5 6 942 8 9 918 2 7 720 4 7 292 7 10 414

Output

8

样例

10 9
81 16 73 7 2 61 86 38 90 28
6 8 725
3 10 12
1 4 558
4 9 615
5 6 942
8 9 918
2 7 720
4 7 292
7 10 414

8