Mojtaba and Arpa are playing a game. They have a list of n numbers in the game.

In a player's turn, he chooses a number pk (where p is a prime number and k is a positive integer) such that pk divides at least one number in the list. For each number in the list divisible by pk, call it x, the player will delete x and add <image> to the list. The player who can not make a valid choice of p and k loses.

Mojtaba starts the game and the players alternatively make moves. Determine which one of players will be the winner if both players play optimally.

Input

The first line contains a single integer n (1 ≤ n ≤ 100) — the number of elements in the list.

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the elements of the list.

Output

If Mojtaba wins, print "Mojtaba", otherwise print "Arpa" (without quotes).

You can print each letter in any case (upper or lower).

Examples

Input

4
1 1 1 1


Output

Arpa


Input

4
1 1 17 17


Output

Mojtaba


Input

4
1 1 17 289


Output

Arpa


Input

5
1 2 3 4 5


Output

Arpa

Note

In the first sample test, Mojtaba can't move.

In the second sample test, Mojtaba chooses p = 17 and k = 1, then the list changes to [1, 1, 1, 1].

In the third sample test, if Mojtaba chooses p = 17 and k = 1, then Arpa chooses p = 17 and k = 1 and wins, if Mojtaba chooses p = 17 and k = 2, then Arpa chooses p = 17 and k = 1 and wins.
#include <bits/stdc++.h>
using namespace std;
void printIntBits2(int num) {
  int bitsNum = (sizeof(int) * 8);
  for (int bit = 0; bit < bitsNum; bit++) {
    int shifted = num >> (bitsNum - bit - 1);
    printf("%d", shifted & 1);
  }
}
map<int, int> g;
int grundy(int mask) {
  if (!mask) return 0;
  if (g.count(mask)) return g[mask];
  set<int> flag;
  for (int i = 0; i < 30; i++)
    if (1 << i <= mask) {
      int newMask = (mask >> i + 1) | (mask & (1 << i) - 1);
      if (newMask < mask) flag.insert(grundy(newMask));
    }
  g[mask] = 0;
  while (flag.count(g[mask])) g[mask]++;
  return g[mask];
}
int main() {
  map<int, int> mp;
  int n;
  scanf("%d", &n);
  for (int k = 0; k < n; ++k) {
    int x;
    scanf("%d", &x);
    for (int j = 2; j * j <= x; ++j)
      if (x % j == 0) {
        int c = 0;
        while (x % j == 0) ++c, x /= j;
        mp[j] |= 1 << (c - 1);
      }
    if (x > 1) mp[x] |= 1;
  }
  int ans = 0;
  map<int, int>::iterator it;
  for (it = mp.begin(); it != mp.end(); ++it) {
    ans ^= grundy(it->second);
  }
  if (!ans)
    cout << "Arpa";
  else
    cout << "Mojtaba";
  return 0;
}
