Bajtazar loves to play the following (single-player) game. On a board, all natural numbers from $a$ to $b$ are written, forming the sequence $$a, a + 1, a + 2, \dots, b - 1, b.$$ Then, zero or more moves are performed. In each move, any two numbers currently on the board are chosen, provided that their sum is an even number. These two chosen numbers are then removed from the board. The goal of the game is to remove as many elements as possible. Help Bajtazar determine this number.

Input

The first and only line of input contains two natural numbers $a, b$ ($1 \le a \le b \le 10^{18}$), representing the beginning and the end of the sequence of numbers with which Bajtazar's game begins.

Output

Your program should output exactly one line containing the maximum number of elements of the sequence that can be removed in the manner described above.

Examples

Input 1

3 7

Output 1

4

Note

For the example, one can, for instance, remove the numbers 3 and 5, and then the numbers 4 and 6.

Subtasks