3094: Berland Square
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Description
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:
