Alice&Brown

Alice and Brown loves games. Today, they will play the following game.

In this game, there are two piles initially consisting of X and Y stones, respectively. Alice and Bob alternately perform the following operation, starting from Alice:

• Take 2i stones from one of the piles. Then, throw away i of them, and put the remaining i in the other pile. Here, the integer i (1≤i) can be freely chosen as long as there is a sufficient number of stones in the pile.

The player who becomes unable to perform the operation, loses the game.

Given X and Y, determine the winner of the game, assuming that both players play optimally.

Constraints

• 0 ≤ X, Y ≤ 10^{18}

Input

Input is given from Standard Input in the following format:

X Y

Output

Print the winner: either Alice or Brown.

Examples

Input

2 1

Output

Brown

Input

5 0

Output

Alice

Input

0 0

Output

Brown

Input

4 8

Output

Alice

inputFormat

Input

Input is given from Standard Input in the following format:

X Y

outputFormat

Output

Print the winner: either Alice or Brown.

Examples

Input

2 1

Output

Brown

Input

5 0

Output

Alice

Input

0 0

Output

Brown

Input

4 8

Output

Alice

样例

0 0

Brown