#include <bits/stdc++.h>
const double pi = acos(-1.0);
using namespace std;
inline long long MAX2(long long a, long long b) {
  return (a) > (b) ? (a) : (b);
}
inline long long MAX3(long long a, long long b, long long c) {
  return (a) > (b) ? ((a) > (c) ? (a) : (c)) : ((b) > (c) ? (b) : (c));
}
inline long long MIN2(long long a, long long b) {
  return (a) < (b) ? (a) : (b);
}
inline long long MIN3(long long a, long long b, long long c) {
  return (a) < (b) ? ((a) < (c) ? (a) : (c)) : ((b) < (c) ? (b) : (c));
}
int mod = 1e9 + 7;
int64_t extGcd(int64_t a, int64_t b, int64_t& x, int64_t& y) {
  if (!a) {
    x = 0;
    y = 1;
    return b;
  }
  int64_t x1, y1;
  int64_t d = extGcd(b % a, a, x1, y1);
  x = y1 - (b / a) * x1;
  y = x1;
  return d;
}
const int factRange = 1000000;
int fact[factRange];
inline int addMod(int a, int b, int m = mod) { return ((int64_t)a + b) % m; }
inline int mulMod(int a, int b, int m = mod) { return ((int64_t)a * b) % m; }
inline int divMod(int a, int b, int m = mod) {
  int64_t x, y;
  int64_t g = extGcd(b, m, x, y);
  if (g != 1) {
    cerr << "Bad gcd!" << '\n';
    for (;;)
      ;
  }
  x = (x % m + m) % m;
  return mulMod(a, x, m);
}
inline long long exp(long long a, long long b) {
  if (a == 0) return 0ll;
  long long r = 1LL;
  while (b > 0) {
    if (b & 1) {
      r = r * (a % mod);
      r = (r + mod) % mod;
    }
    b /= 2;
    a = (a % mod) * (a % mod);
    a = (a + mod) % mod;
  }
  return (r + mod) % mod;
}
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  if (a == 0) return b;
  return gcd(b, a % b);
}
inline long long poww(long long a, long long b) {
  long long r = 1LL;
  while (b > 0) {
    if (b & 1) r = r * a;
    b /= 2;
    a = a * a;
  }
  return (long long)r;
}
unsigned long int setbits(long long n) {
  unsigned long int count = 0;
  while (n) {
    n &= (n - 1);
    count++;
  }
  return count;
}
int main() {
  int n;
  cin >> n;
  long long a[n];
  int flag = 0;
  for (long long i = (long long)(0); i < (long long)(n); i++) cin >> a[i];
  for (long long i = (long long)(0); i < (long long)(n); i++) {
    while (a[i] % 2 == 0) a[i] /= 2;
    while (a[i] % 3 == 0) a[i] /= 3;
  }
  for (long long i = (long long)(1); i < (long long)(n); i++)
    if (a[i] != a[0]) {
      flag = 1;
      break;
    }
  if (flag)
    cout << "No" << '\n';
  else
    cout << "Yes" << '\n';
  return 0;
}

### Prompt

Generate a cpp solution to the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
const double pi = acos(-1.0);
using namespace std;
inline long long MAX2(long long a, long long b) {
  return (a) > (b) ? (a) : (b);
}
inline long long MAX3(long long a, long long b, long long c) {
  return (a) > (b) ? ((a) > (c) ? (a) : (c)) : ((b) > (c) ? (b) : (c));
}
inline long long MIN2(long long a, long long b) {
  return (a) < (b) ? (a) : (b);
}
inline long long MIN3(long long a, long long b, long long c) {
  return (a) < (b) ? ((a) < (c) ? (a) : (c)) : ((b) < (c) ? (b) : (c));
}
int mod = 1e9 + 7;
int64_t extGcd(int64_t a, int64_t b, int64_t& x, int64_t& y) {
  if (!a) {
    x = 0;
    y = 1;
    return b;
  }
  int64_t x1, y1;
  int64_t d = extGcd(b % a, a, x1, y1);
  x = y1 - (b / a) * x1;
  y = x1;
  return d;
}
const int factRange = 1000000;
int fact[factRange];
inline int addMod(int a, int b, int m = mod) { return ((int64_t)a + b) % m; }
inline int mulMod(int a, int b, int m = mod) { return ((int64_t)a * b) % m; }
inline int divMod(int a, int b, int m = mod) {
  int64_t x, y;
  int64_t g = extGcd(b, m, x, y);
  if (g != 1) {
    cerr << "Bad gcd!" << '\n';
    for (;;)
      ;
  }
  x = (x % m + m) % m;
  return mulMod(a, x, m);
}
inline long long exp(long long a, long long b) {
  if (a == 0) return 0ll;
  long long r = 1LL;
  while (b > 0) {
    if (b & 1) {
      r = r * (a % mod);
      r = (r + mod) % mod;
    }
    b /= 2;
    a = (a % mod) * (a % mod);
    a = (a + mod) % mod;
  }
  return (r + mod) % mod;
}
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  if (a == 0) return b;
  return gcd(b, a % b);
}
inline long long poww(long long a, long long b) {
  long long r = 1LL;
  while (b > 0) {
    if (b & 1) r = r * a;
    b /= 2;
    a = a * a;
  }
  return (long long)r;
}
unsigned long int setbits(long long n) {
  unsigned long int count = 0;
  while (n) {
    n &= (n - 1);
    count++;
  }
  return count;
}
int main() {
  int n;
  cin >> n;
  long long a[n];
  int flag = 0;
  for (long long i = (long long)(0); i < (long long)(n); i++) cin >> a[i];
  for (long long i = (long long)(0); i < (long long)(n); i++) {
    while (a[i] % 2 == 0) a[i] /= 2;
    while (a[i] % 3 == 0) a[i] /= 3;
  }
  for (long long i = (long long)(1); i < (long long)(n); i++)
    if (a[i] != a[0]) {
      flag = 1;
      break;
    }
  if (flag)
    cout << "No" << '\n';
  else
    cout << "Yes" << '\n';
  return 0;
}

```