Problem J: Merry Christmas

International Christmas Present Company (ICPC) is a company to employ Santa and deliver presents on Christmas. Many parents request ICPC to deliver presents to their children at specified time of December 24. Although same Santa can deliver two or more presents, because it takes time to move between houses, two or more Santa might be needed to finish all the requests on time.

Employing Santa needs much money, so the president of ICPC employed you, a great program- mer, to optimize delivery schedule. Your task is to write a program to calculate the minimum number of Santa necessary to finish the given requests on time. Because each Santa has been well trained and can conceal himself in the town, you can put the initial position of each Santa anywhere.

Input

The input consists of several datasets. Each dataset is formatted as follows.

N M L
u₁ v₁ d₁
u₂ v₂ d₂
.
.
.
u_M v_M d_M
p₁ t₁
p₂ t₂
.
.
.
p_L t_L

The first line of a dataset contains three integer, N , M and L (1 ≤ N ≤ 100, 0 ≤ M ≤ 1000, 1 ≤ L ≤ 1000) each indicates the number of houses, roads and requests respectively.

The following M lines describe the road network. The i-th line contains three integers, u_i , v_i , and d_i (0 ≤ u_i < v_i ≤ N - 1, 1 ≤ d_i ≤ 100) which means that there is a road connecting houses u_i and v_i with d_i length. Each road is bidirectional. There is at most one road between same pair of houses. Whole network might be disconnected.

The next L lines describe the requests. The i-th line contains two integers, p_i and t_i (0 ≤ p_i ≤ N - 1, 0 ≤ t_i ≤ 10⁸ ) which means that there is a delivery request to house p_i on time t_i . There is at most one request for same place and time. You can assume that time taken other than movement can be neglectable, and every Santa has the same speed, one unit distance per unit time.

The end of the input is indicated by a line containing three zeros separated by a space, and you should not process this as a test case.

Output

Print the minimum number of Santa necessary to finish all the requests on time.

Sample Input

3 2 3
0 1 10
1 2 10
0 0
1 10
2 0
3 2 4
0 1 10
1 2 10
0 0
1 10
2 20
0 40
10 10 10
0 1 39
2 3 48
3 5 20
4 8 43
3 9 10
8 9 40
3 4 5
5 7 20
1 7 93
1 3 20
0 0
1 100000000
2 100
3 543
4 500
5 400
6 300
7 200
8 100
9 100
0 0 0

Output for the Sample Input

2
1
4

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