CSES - Forbidden Cities
• Time limit: 1.00 s
• Memory limit: 512 MB
There are $n$ cities and $m$ roads between them. Kaaleppi is currently in city $a$ and wants to travel to city $b$.

However, there is a problem: Kaaleppi has recently robbed a bank in city $c$ and can't enter the city, because the local police would catch him. Your task is to find out if there is a route from city $a$ to city $b$ that does not visit city $c$.

As an additional challenge, you have to process $q$ queries where $a$, $b$ and $c$ vary.

Input

The first input line has three integers $n$, $m$ and $q$: the number of cities, roads and queries. The cities are numbered $1,2,\dots,n$.

Then, there are $m$ lines describing the roads. Each line has two integers $a$ and $b$: there is a road between cities $a$ and $b$. Each road is bidirectional.

Finally, there are $q$ lines describing the queries. Each line has three integers $a$, $b$ and $c$: is there a route from city $a$ to city $b$ that does not visit city $c$?

You can assume that there is a route between any two cities.

Output

For each query, print "YES", if there is such a route, and "NO" otherwise.

Constraints
• $1 \le n \le 10^5$
• $1 \le m \le 2 \cdot 10^5$
• $1 \le q \le 10^5$
• $1 \le a,b,c \le n$
Example

Input:
5 6 3 1 2 1 3 2 3 2 4 3 4 4 5 1 4 2 3 5 4 3 5 2

Output:
YES NO YES