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;
map<int, int> SG;
map<int, int> masks;
int N;
int sg(int num) {
  set<int> S;
  if (SG.count(num)) return SG[num];
  for (int bit = 0;; bit++) {
    if (!(num >> bit)) break;
    int a = (num >> (bit + 1));
    int b = num & ((1 << (bit)) - 1);
    S.insert(sg(a | b));
  }
  int f = 0;
  while (S.count(f)) f++;
  return SG[num] = f;
}
int main() {
  scanf("%d", &N);
  for (int i = 1; i <= N; i++) {
    int val;
    scanf("%d", &val);
    for (int j = 2; 1LL * j * j <= val; j++) {
      if (val % j == 0) {
        int e = 0;
        while (val % j == 0) {
          val /= j;
          e++;
        }
        masks[j] |= (1 << (e - 1));
      }
    }
    if (val > 1) masks[val] |= 1;
  }
  int xo = 0;
  for (auto it : masks) {
    xo ^= sg(it.second);
  }
  fputs(xo == 0 ? "Arpa" : "Mojtaba", stdout);
  return 0;
}
