Algorithms and Data Structures

Match the dancers

There are n men and k women with corresponding dancing skills and .
You’d like to match them in pairs and to make sure both partners are satisfied, you’d like to keep the difference in skill levels for each pair at most 1.
How many pairs would it be possible to have for the dancing competition?
 
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Input

The first line of the input contains two integers n and k (1 ≤ n, k ≤ ).
The next line contains n space-separated integers (1 ≤ ≤ 100).
The third line contains k space-separated integers (1 ≤ ≤ 100).

Output

The program should print the maximum number of pairs you can get by matching them.

Examples

Input
Output
4 5 2 4 6 3 5 1 5 7 10
3
4 4 1 2 3 4 51 52 53 54
0
5 3 2 2 2 2 2 2 3 4
2

Explanation

  1. Match → 2 ↔ 1, 4 ↔ 5, and 6 ↔ 5
  1. Not possible to match anyone
  1. Match → 2 ↔ 2, 2 ↔ 3

Constraints

Time limit: 0.2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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