## Problem Description

The city of Catville has come under attack! The structure of Catville can be described as a series of N intersections, with E roads, and each road i connecting two intersections Si and Ti.

A total of B bombs have been dropped on Catville, and the ith bomb has been dropped at intersection Xi with a power of Yi. The power of a bomb decides the extent of damage it can cause. A power 1 bomb will only damage the intersection it lands on, a power 2 bomb will damage the intersection it lands on as well as its neighbours, and so on. In general, a power x bomb will damage all intersections that are reachable from Xi with less than x roads.

After the attack, the mayor of Catville wants to know, how many intersections of Catville have been damaged.

## Input

The first line of input will contain three integers, N, E and B.

The next E lines of input will contain two integers each, Si and Ti.

The next B lines of input will contain two integers each, Xi and Yi.

## Output

The output should contain one line with one integer, the number of damaged intersections.

## Limits

For all subtasks: 1 ≤ B ≤ N ≤ 500 000, 1 ≤ E ≤ 1 000 000, 1 ≤ Si, Ti, Xi ≤ N, 1 ≤ Yi < N. No two bombs will fall on the same spot.

Subtask 1 (3%): Yi = 1.

Subtask 2 (9%): 1 ≤ N ≤ 1 000, E = N - 1, Si = i, Ti = i + 1.

Subtask 3 (15%): 1 ≤ N ≤ 1 000, 1 ≤ E ≤ 2 000.

Subtask 4 (18%): B = 1.

Subtask 5 (11%): E = N - 1, Si = i, Ti = i + 1.

Subtask 6 (10%): E = N, Si = i, Ti = i % N + 1.

Subtask 7 (13%): 1 ≤ N ≤ 100 000, 1 ≤ E ≤ 200 000.

```6 6 2
1 2
2 3
2 4
3 5
4 6
5 6
3 2
5 2```

`4`

```5 4 2
1 2
2 3
3 4
4 5
3 1
4 3```

## Sample Output 2

`4`

### Submitting .cpp to 'bombing'

Time Limit: 2 Seconds
Memory Limit: 256MB
Source: Dunjudge Archive

1 3
2 9
3 15
4 18
5 11
6 10
7 13
8 21
9 0