Codeforces 574C Bear and Poker【思维】

C. Bear and Poker

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Limak is an old brown bear. He often plays poker with his friends. Today they went to a casino. There aren 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?

Input

First line of input contains an integer n (2 ≤ n ≤ 10⁵), the number of players.

The second line contains n integer numbersa₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁹) — the bids of players.

Output

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

Examples

Input

475 150 75 50

Output

Yes

Input

3100 150 250

Output

No

Note

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.

题目大意：

给你N个数，每个数都可以进行无限次数的*2或者是*3.

问最终能否使得所有数都相等。

思路：

逆向思维，向上乘，我们不如改变成向下除，乘除等价，我们只要将所有数都无脑/2直到不能除为止开始/3.直到不能除为止。

那么剩下的这个序列如果所有数都相等，那么就是Yes，否则就是No

Ac代码：

#include<stdio.h>#include<string.h>#include<algorithm>using namespace std;int a[100505];int main(){    int n;    while(~scanf("%d",&n))    {        for(int i=1;i<=n;i++)        {            scanf("%d",&a[i]);        }        for(int i=1;i<=n;i++)        {            while(a[i]%2==0)a[i]/=2;            while(a[i]%3==0)a[i]/=3;        }        int flag=0;        sort(a+1,a+1+n);        for(int i=2;i<=n;i++)        {            if(a[i]!=a[i-1])flag=1;        }        if(flag==0)printf("Yes\n");        else printf("No\n");    }}