### ** bombing**

## 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 *S*_{i} and *T*_{i}.

A total of *B* bombs have been dropped on Catville, and the *i*th bomb has been dropped at intersection *X*_{i} with a power of *Y*_{i}. 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 *X*_{i} 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, *S*_{i} and *T*_{i}.

The next *B* lines of input will contain two integers each, *X*_{i} and *Y*_{i}.

## 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 ≤ S_{i}, T_{i}, X_{i} ≤ N, 1 ≤ Y_{i} < N. No two bombs will fall on the same spot.

Subtask 1 (3%): Y_{i} = 1.

Subtask 2 (9%): 1 ≤ N ≤ 1 000, E = N - 1, S_{i} = i, T_{i} = i + 1.

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

Subtask 4 (18%): B = 1.

Subtask 5 (11%): E = N - 1, S_{i} = i, T_{i} = i + 1.

Subtask 6 (10%): E = N, S_{i} = i, T_{i} = i % N + 1.

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

Subtask 8 (21%): No additional constraints.

Subtask 9 (0%): Sample Testcases.

## Sample Input 1

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

## Sample Output 1

4

## Sample Input 2

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

## Sample Output 2

4