MATCHING - Fast Maximum Matching


FJ has N (1 ≤ N ≤ 50,000) cows and M (1 ≤ M ≤ 50,000) bulls. Given a list of P (1 ≤ P ≤ 150,000) potential matches between a cow and a bull, compute the greatest number of pairs that can be matched. Of course, a cow can be matched to at most one bull, and vice versa.

Input

The first line contains three integers, N, M, and P. Each of the next P lines contains two integers A (1 ≤ A ≤ N) and B (1 ≤ B ≤ M), denoting that cow A can be matched with bull B.

Output

Print a single integer that is the maximum number of pairs that can be obtained.

Example

Input:
5 4 6
5 2
1 2
4 3
3 1
2 2
4 4

Output:
3

Cow 1 can be matched to bull 2, cow 3 to bull 1, and cow 4 to bull 3.

Note: see also http://www.spoj.com/problems/FASTFLOW/.


hide comments
Brian Bi: 2010-01-12 05:37:43

Are there duplicate pairs in input?


Added by:Neal Wu
Date:2009-04-12
Time limit:0.400s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO