J. JP's List of Trips
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

JP is coordinating a bus agency which is responsible for all the bus drivers of the state, as well as all the trips that their buses do.

A trip is always between two distinct cities, and is defined by the roads that the bus driver takes departing from the starting city and ending in the destination city, no road should be repeated in the path of a trip.

Because bus drivers are very creative, they find it boring to stick to rules when driving, they don't like to "take the shortest path", or "always visit cities with lower index" so it is very difficult to predict what their trip will look like, but JP believes there should be a way to know for some cities what is the trip a bus driver will take, so he brought to you a list with all the possible buses trips, and asked for your help.

Help JP to find for each possible trip in his list if he can be sure on what path a bus driver will take between the cities on the trip.

Input

The first line of input contains three integer numbers, $$$N$$$, $$$M$$$ and $$$Q$$$ $$$\left(2 \leq N \leq 10^{5}, N - 1 \leq M \leq \min\left\{10^{5}, \frac{N(N - 1)}{2}\right\}, 1 \leq Q \leq 10^{5}\right)$$$ representing the number of cities, the number of roads and the number of trips in JP's list, respectively.

Each of the following $$$M$$$ lines contains two integers $$$A$$$ and $$$B$$$ ($$$1 \leq A, B \leq N$$$) describing a road between cities $$$A$$$ and $$$B$$$. It is guaranteed that it is possible to reach each city from any other city.

Each of the following $$$Q$$$ lines contains two different integer numbers separated by a space, $$$S$$$, and $$$E$$$, ($$$1 \leq S, E \leq N$$$), describing a trip in JPs list.

Output

Output $$$Q$$$ lines, where the $$$i$$$-th line contains the answer to the $$$i$$$-th trip in JPs list, being "YES" if he can be sure of what the path in the trip will or "NO" if he can't be sure.

Examples
Input
5 4 3
1 2
5 4
3 1
2 5
1 3
5 3
3 4
Output
YES
YES
YES
Input
4 4 1
1 2
2 3
3 4
4 1
1 2
Output
NO