SOLVE

LATER

Two paths

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Given an undirected graph with *n* vertices and *m* edges. Each edge is one of the two types: white and black.

There are *q* queries denoted by four vertices *a*, *b*, *c* and *d*. Each query asks: can some of the black edges be deleted, so that *a* is reachable from *b*, but *c* is not reachable from *d*? Note that graph itself doesn't change from query to query.

**Input format**

The first line contains three integers *n*, *m* and *q* (\(1 \leq n, m, q \leq 2 \cdot 10^5\)) - number of vertices, number of edges and number of queries, respectively.

Then *m* lines follow.

The *i*-th of them contains three integers \(a_i\), \(b_i\) and \(t_i\) (\(1 \leq a_i, b_i \leq n\), \(a_i \neq b_i\), \(t_i \in {0, 1}\)) describing edge connecting \(a_i\) and \(b_i\), \(t_i = 0\) for black edge and \(t_i = 1\) for white edge.

Then *q* lines follow.

The *i*-th of them contains four integers \(a_i\), \(b_i\), \(c_i\) and \(d_i\) (\(1 \leq a_i, b_i, c_i, d_i \leq n\) — vertices in the *i*-th query.

**Output format**

For each query print `Yes`

if it's possible to delete some black edges and satisfy the condition. Print `No`

otherwise.

Explanation

- In the first query you can delete the 6-th edge (between 4 and 5).
- In the second query you can delete first, second and 4-th edges.

Time Limit:
2.0 sec(s)
for each input file.

Memory Limit:
512 MB

Source Limit:
1024 KB