The third one is extra#5280

The third one is extra

2 seconds
256 megabytes
Hard

Zhenya, Zhenyechka, and Yevhen are playing an interesting game. On the table lie candies of types. During each turn, a player may take any number of candies of one type and eat them. The turns proceed in the following order: Zhenya, then Zhenyechka, then Yevhen. The player who takes the last candy wins the game.

Zhenya would like his friend Zhenyechka to win. Can he guarantee her victory, regardless of the moves made by her and Yevhen?

Input

The first line contains an integer — the number of types of candies.

The second line contains natural numbers a_1, a_2, \ldots, a_n, where a_i is the number of candies of the -th type.

The following constraint holds:

(a_1 + 1)(a_2 + 1)\cdots(a_n + 1) \leq 100.

Output

Print **"Yes"** if Zhenya can guarantee Zhenyechka's victory, or **"No"** otherwise.

Examples

Example 1

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