Description

有两个玩家，会去挑选一些数字，每次只能选至少与一个0相邻的数字（不能选0），拿完一个数字后这个数字 会变成0。 两个玩家都采取最优策略，使自己拿到的数字的和最大，问最后两位玩家的得分。 数字个数< 1000000，保证初始时至少有一个0。

Format

Input

Output

Samples

8
1 2 0 3 7 4 0 9

17 9

Limitation

Explanation of the example: The fence consisted of 8 planks, out of which 2 have already been eaten. The first termite in his first turn can choose between planks of heights 2, 3, 4 and 9. During the optimal game, in the consecutive turns, termites will eat planks of heights 9, 2, 1, 4, 7 and 3.