3196. Wormholes

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 $N$ $(1 \leq N \leq 500)$ fields conveniently numbered $1$..$N$, $M$ $(1 \leq M \leq 2500)$ paths, and $W$ $(1 \leq W \leq 200)$ 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 $F$ $(1 \leq F \leq 5)$ 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.

输入格式

• Line $1$: A single integer, $F$. $F$ farm descriptions follow.
• Line $1$ of each farm: Three space-separated integers respectively: $N, M, W$
• Lines $2$.. $M+1$ 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 $M+2$..$M+ W+1$ 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.

输出格式

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

样例

Input
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

Output
NO
YES


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