Saturday 24 October 2015

A. 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.
We can numltiply any number with 2 and 3 any number of times that means in general a number can be multiplied with 2^p*3^q. As each number can be broken in prime as 
x=2^a*3^b*5^c*7^d 
therefore intuitively we can increase a and and b to any number we want but the rest must be same. Hence the solution is that all numbers should have same powers of other terms except 2 and 3 

code


#include<bits/stdc++.h>
using namespace std;
int a[100010];
int main()
{
int n;
cin>>n;
for(int i=0;i<n;i++)
{
cin>>a[i];
}
for(int i=0;i<n;i++)
{
    while(a[i]%2==0)
    a[i]/=2;
    while(a[i]%3==0)
    a[i]/=3;
}

bool f=0;
for(int i=1;i<n;i++)
{
   if(a[i]!=a[0])
   {
    f=1;
    break;
}
}
if(f)
cout<<"No"<<endl;
else
cout<<"Yes"<<endl;
return 0;
}

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