Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Berland Square

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLast 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:

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/15/2019 08:24:09 (f2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|