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Problem Statement

There are $N$ points and $M$ segments on the $xy$-plane. Each segment connects two of these points and they don't intersect each other except at the endpoints. You are also given $Q$ points as queries. Your task is to determine for each query point whether you can make a polygon that encloses the query point using some of the given segments. Note that the polygon should not necessarily be convex.

Input

Each input is formatted as follows.

$N$ $M$ $Q$
$x\_1$ $y\_1$
...
$x\_N$ $y\_N$
$a\_1$ $b\_1$
...
$a\_M$ $b\_M$
$qx\_1$ $qy\_1$
...
$qx\_Q$ $qy\_Q$

The first line contains three integers $N$ ($2 \\leq N \\leq 100{,}000$), $M$ ($1 \\leq M \\leq 100{,}000$), and $Q$ ($1 \\leq Q \\leq 100{,}000$), which represent the number of points, the number of segments, and the number of queries, respectively. Each of the following $N$ lines contains two integers $x\_i$ and $y\_i$ ($-100{,}000 \\leq x\_i, y\_i \\leq 100{,}000$), the coordinates of the $i$-th point. The points are guaranteed to be distinct, that is, $(x\_i, y\_i) \\neq (x\_j, y\_j)$ when $i \\neq j$. Each of the following $M$ lines contains two integers $a\_i$ and $b\_i$ ($1 \\leq a\_i \\lt b\_i \\leq N$), which indicate that the $i$-th segment connects the $a\_i$-th point and the $b\_i$-th point. Assume that those segments do not intersect each other except at the endpoints. Each of the following $Q$ lines contains two integers $qx\_i$ and $qy\_i$ ($-100{,}000 \\leq qx\_i, qy\_i \\leq 100{,}000$), the coordinates of the $i$-th query point.

You can assume that, for any pair of query point and segment, the distance between them is at least $10^{-4}$.

Output

The output should contain $Q$ lines. Print "Yes" on the $i$-th line if there is a polygon that contains the $i$-th query point. Otherwise print "No" on the $i$-th line.

Sample Input 1

4 5 3
-10 -10
10 -10
10 10
-10 10
1 2
1 3
1 4
2 3
3 4
-20 0
1 0
20 0```

### Output for the Sample Input 1

```plain
No
Yes
No```

* * *

### Sample Input 2

```plain
8 8 5
-20 -20
20 -20
20 20
-20 20
-10 -10
10 -10
10 10
-10 10
1 2
1 4
2 3
3 4
5 6
5 8
6 7
7 8
-25 0
-15 0
0 0
15 0
25 0```

### Output for the Sample Input 2

```plain
No
Yes
Yes
Yes
No```

* * *

### Sample Input 3

```plain
8 8 5
-20 -10
-10 -10
-10 10
-20 10
10 -10
20 -10
20 10
10 10
1 2
2 3
3 4
1 4
5 6
6 7
7 8
5 8
-30 0
-15 0
0 0
15 0
30 0```

### Output for the Sample Input 3

```plain
No
Yes
No
Yes
No```

* * *