uniquepath

Problem Statement

Snuke's mother gave Snuke an undirected graph consisting of N vertices numbered 0 to N-1 and M edges. This graph was connected and contained no parallel edges or self-loops.

One day, Snuke broke this graph. Fortunately, he remembered Q clues about the graph. The i-th clue (0 ≤ i ≤ Q-1) is represented as integers A_i,B_i,C_i and means the following:

• If C_i=0: there was exactly one simple path (a path that never visits the same vertex twice) from Vertex A_i to B_i.
• If C_i=1: there were two or more simple paths from Vertex A_i to B_i.

Snuke is not sure if his memory is correct, and worried whether there is a graph that matches these Q clues. Determine if there exists a graph that matches Snuke's memory.

Constraints

• 2 ≤ N ≤ 10⁵
• N-1 ≤ M ≤ N × (N-1)/2
• 1 ≤ Q ≤ 10⁵
• 0 ≤ A_i,B_i ≤ N-1
• A_i ≠ B_i
• 0 ≤ C_i ≤ 1
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M Q
A0 B0 C0
A1 B1 C1

.
.
.

AQ-1 BQ-1 CQ-1

Output

If there exists a graph that matches Snuke's memory, print Yes; otherwise, print No.

Sample Input 1

5 5 3
0 1 0
1 2 1
2 3 0

Sample Output 1

Yes

For example, consider a graph with edges (0,1),(1,2),(1,4),(2,3),(2,4). This graph matches the clues.

Sample Input 2

4 4 3
0 1 0
1 2 1
2 3 0

Sample Output 2

No

Sample Input 3

10 9 9
7 6 0
4 5 1
9 7 0
2 9 0
2 3 0
4 1 0
8 0 0
9 1 0
3 0 0

Sample Output 3

No