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).

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->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.

Source

USACO 2006 December Gold