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