Codeforces Round #318 574C Bear and Elections(脑洞)

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 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.

Sample test(s)

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.

给一个长度为n的数组，每个数可以变成自身的2或3倍，问你能否将这n个数变为一个数。

由于每次都是变成自己的2或3倍，所以读入进来的某个数除2或3后均能变成一个数，否则就不能变成一个数。

AC代码：

#include "iostream"
#include "cstdio"
#include "cstring"
#include "algorithm"
#include "set"
using namespace std;
const int MAXN = 1e5 + 5;
int main(int argc, char const *argv[])
{
	int n;
	set<int> s;
	scanf("%d", &n);
	for(int i = 0; i < n; ++i) {
		int x;
		scanf("%d", &x);
		while(x % 3 == 0) x /= 3;
		while(x % 2 == 0) x /= 2;
		s.insert(x);
	}
	if(s.size() == 1) printf("Yes\n");
	else printf("No\n");
	return 0;
}