C. Berland Square
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Last year the world's largest square was built in Berland. It is known that the square can be represented as an infinite plane with an introduced Cartesian system of coordinates. On that square two sets of concentric circles were painted. Let's call the set of concentric circles with radii 1, 2, ..., K and the center in the point (z, 0) a (K, z)-set. Thus, on the square were painted a (N, x)-set and a (M, y)-set. You have to find out how many parts those sets divided the square into.

Input

The first line contains integers N, x, M, y. (1 ≤ N, M ≤ 100000,  - 100000 ≤ x, y ≤ 100000, x ≠ y).

Output

Print the sought number of parts.

Examples
Input
1 0 1 1
Output
4
Input
1 0 1 2
Output
3
Input
3 3 4 7
Output
17
Note

Picture for the third sample: