Taco Path Query

You are given a weighted undirected graph consisting of N stones (vertices) and M magical paths (edges). Each magical path connects two stones and has an associated energy value. You are also given Q queries. Each query consists of three integers U, V, and W: you must determine whether there exists a simple path (i.e. no stone is visited more than once) from stone U to stone V such that the total sum of the energies along the path is at least W.

The energy sum along a path is calculated as:

[ \sum_{(i,j) \in path} E_{ij} \geq W ]

If such a path exists, print YES, otherwise, print NO.

inputFormat

The first line contains three space-separated integers: N (number of stones), M (number of magical paths), and Q (number of queries).

The next M lines each contain three space-separated integers: A B E, representing a magical path between stone A and stone B with energy value E.

The next Q lines each contain three space-separated integers: U V W, representing a query asking whether there is a path from stone U to stone V whose total magical energy is at least W.

outputFormat

For each query, output a single line containing YES if such a path exists, and NO otherwise.

## sample

6 7 3
1 2 4
2 3 5
3 4 10
4 5 1
5 6 3
1 6 7
2 5 9
1 5 15
2 6 8
4 1 10

NO
YES
YES

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