Chessboard

Limits: 2 sec., 512 MiB

This statement was translated automatically from Ukrainian.

There is an \(n \times m\) chessboard (\(n\) rows and \(m\) columns). The top-left cell of the board is white, and Zenik is standing on it.

Zenik wants to get from the top-left corner to the bottom-right corner, but Zenik can only move on white cells. Initially, Zenik can choose some rows and invert the colors of all cells in the chosen rows. After that, he can choose some columns and invert the colors of all cells in the chosen columns.

For example, if Zenik applies this operation to the third row, it looks like this:

Note that since Zenik only moves on white cells, after his operations the top-left cell must remain white. What is the minimum number of rows and columns Zenik needs to choose to reach the bottom-right corner?

Input

The first line contains two integers \(n\) and \(m\) — the height and width of the chessboard.

Output

Print a single integer — the minimum number of rows and columns to change in order to reach the bottom-right cell.

Constraints

\(1 \le n, m \le 10^9\).

Scoring consists of the following blocks:

• 1 point for each example from the statement,

• 40 points: \(n = 1\),

• 58 points: no additional constraints.

You will get the points for a block only if your program passes all tests in that block.

Samples

Input (stdin) сopy	Output (stdout) сopy
1 5	2

Input (stdin) сopy	Output (stdout) сopy
3 3	2

Notes

In the first example, Zenik can choose the second and fourth columns.