The Parquet of the Triangles

We laid by three-cornered tiles the rectangular room with sides M to N (at first for hori-zontal lines, and then for vertical lines) and we numbered it as shown on the picture.

It is possible to move from one parquet to another through a general side only for one step. Find the least quantity of steps, which necessary for transferring from parquet A to parquet B.

Input

In the input file in the first line through the gap is set to M, N (1 ≤ M, N ≤ 100), and the second - A, B. Output The desired number of steps.

Examples