## 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 ≤ *N* ≤ 500) fields conveniently numbered 1..*N*, *M* (1 ≤ *M* ≤ 2500) paths, and *W* (1 ≤ *W* ≤ 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 ≤ *F* ≤ 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:

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..

*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.

## Output:

Lines 1..

*F*: For each farm, output "YES" if FJ can achieve his goal, otherwise output "NO" (do not include the quotes).

## Sample 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

## Sample Output:

NO
YES

## Note:

For farm 1, FJ cannot travel back in time.

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