## 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 4Output: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/.

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 |