Best matcher
You’ve decided to implement the simplest version of a dating app. For that, you’ve decided to collect the heights of individuals in Group A as and the heights of individuals in Group B as . You’ve decided to match as many pairs as possible (one person can only be matched once). And you think that couples will be okay if:
- The person from Group B is not shorter than the person from Group A by
xand
- The person from Group B is not taller than the person from Group A by more than
y.
You’d like to match as many pairs as possible.
Input
The first line of the input contains 4 integers
n, m (1 ≤ n, m ≤ ), x, and y (0 ≤ x, y ≤ ) - the number of individuals in Group A, the number of individuals in Group B, and the bounds for acceptable heights.The next line contains n integers representing the heights of the individuals in Group A (1 ≤ ≤ ).
The line after that contains m integers representing the heights of the individuals in Group B (1 ≤ ≤ ).
Output
The program should print the maximum number of pairs matched.
Examples
Input | Output |
6 2 0 0
1 2 3 4 5 6
6 7 | 1 |
3 3 1 1
4 5 6
3 4 7 | 3 |
Constraints
Time limit: 2 seconds
Memory limit: 512 MB
Output limit: 1 MB