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.
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.
For each query, print "YES", if there is such a route, and "NO" otherwise.
5 6 3 1 2 1 3 2 3 2 4 3 4 4 5 1 4 2 3 5 4 3 5 2· · \n · \n · \n · \n · \n · \n · \n · · \n · · \n · · \n
YES NO YES\n \n \n