Bear and Poker

题意翻译

有$n$ 个数$a_i$ ，你可以把每个数任意次$\times 2$ 或$\times 3$ ，问能否最终使得每个数相等。

题目描述

Limak is an old brown bear. He often plays poker with his friends. Today they went to a casino. There are $ n $ players (including Limak himself) and right now all of them have bids on the table. $ i $ -th of them has bid with size $ a_{i} $ dollars. Each player can double his bid any number of times and triple his bid any number of times. The casino has a great jackpot for making all bids equal. Is it possible that Limak and his friends will win a jackpot?

输入输出格式

输入格式

First line of input contains an integer $ n $ ( $ 2<=n<=10^{5} $ ), the number of players. The second line contains $ n $ integer numbers $ a_{1},a_{2},...,a_{n} $ ( $ 1<=a_{i}<=10^{9} $ ) — the bids of players.

输出格式

Print "Yes" (without the quotes) if players can make their bids become equal, or "No" otherwise.

输入输出样例

输入样例 #1

4
75 150 75 50

输出样例 #1

Yes

输入样例 #2

3
100 150 250

输出样例 #2

No

说明

In the first sample test first and third players should double their bids twice, second player should double his bid once and fourth player should both double and triple his bid. It can be shown that in the second sample test there is no way to make all bids equal.

题意翻译

有$n$ 个数$a_i$ ，你可以把每个数任意次$\times 2$ 或$\times 3$ ，问能否最终使得每个数相等。