Codeforces-573A-Bear and Poker

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 ai 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 numbers a1, a2, …, an (1 ≤ ai ≤ 109) — the bids of players.

Output

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

Examples

Input

4

75 150 75 50

Output

Yes

Input

3

100 150 250

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.

给你n个数，然后问他们3倍，2倍都能否相等，不限次数。

一开始想的gcd和lcm去套，然后脑跑总是gg，最后发现X3或者X2和/3和/2是一样一样的，直接算除法就好

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<set>
using namespace std;

set<int>s;
int a[100005];

int main()
{
int n;
while(scanf("%d",&n)!=EOF)
{
s.clear();
for(int i=0;i<n;i++) scanf("%d",&a[i]);
for(int i=0;i<n;i++)
{
while(a[i]%3==0) a[i]=a[i]/3;
while(a[i]%2==0) a[i]=a[i]/2;
s.insert(a[i]);
}
if(s.size()==1)
printf("Yes\n");
else printf("No\n");
}
return 0;
}