Description

While exploring his many farms, Farmer John has discovered a number of amazing wormholes. A wormhole is very peculiar because it is a one-way path that delivers you to its destination at a time that is BEFORE you entered the wormhole! Each of FJ's farms comprises $N (1 \le N \le 500)$ fields conveniently numbered $1 \sim N, M (1 \le M \le 2500)$ paths, and $W (1 \le W \le 200)$ wormholes.

As FJ is an avid time-traveling fan, he wants to do the following: start at some field, travel through some paths and wormholes, and return to the starting field a time before his initial departure. Perhaps he will be able to meet himself :) .

To help FJ find out whether this is possible or not, he will supply you with complete maps to $F (1 \le F \le 5)$ of his farms. No paths will take longer than $10,000$ seconds to travel and no wormhole can bring FJ back in time by more than $10,000$ seconds.

Input Format

Line $1$: A single integer, $F$. $F$ farm descriptions follow.

Line $1$ of each farm: Three space-separated integers respectively: $N$, $M$, and $W$.

Lines $2 \sim M+1$ of each farm: Three space-separated numbers $(S, E, T)$ that describe, respectively: a bidirectional path between $S$ and $E$ that requires $T$ seconds to traverse. Two fields might be connected by more than one path.

Lines $M+2 \sim M+W+1$ of each farm: Three space-separated numbers $(S, E, T)$ that describe, respectively: A one way path from $S$ to $E$ that also moves the traveler back $T$ seconds.

Output Format

Lines $1 \sim F$: For each farm, output YES if FJ can achieve his goal, otherwise output NO.

2
3 3 1
1 2 2
1 3 4
2 3 1
3 1 3
3 2 1
1 2 3
2 3 4
3 1 8

NO
YES

Hint

For farm $1$, FJ cannot travel back in time.

For farm $2$, FJ could travel back in time by the cycle $1 \to 2 \to 3 \to 1$, arriving back at his starting location $1$ second before he leaves. He could start from anywhere on the cycle to accomplish this.