### 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 Ai,Bi,Ci and means the following:

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

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 ≤ Ai,Bi ≤ N-1
• Ai ≠ Bi
• 0 ≤ Ci ≤ 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`.

```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.

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

```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
```

```No
```

### Submitting .cpp to 'uniquepath'

Time Limit: 1 Seconds
Memory Limit: 1024MB
No. of ACs: 10