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;
const int MAXN = 110, WI = 30;
int n, a[MAXN];
map<int, int> sg;
int getsg(int x) {
  if (sg.count(x))
    return sg[x];
  else {
    bool cov[WI];
    memset(cov, 0, sizeof(cov));
    for (int i = 0; i < WI; i++) {
      int y = 0;
      for (int j = 0; j < WI; j++) {
        if (j < i && ((x >> j) & 1)) y |= 1 << j;
        if (j > i && ((x >> j) & 1)) y |= 1 << (j - i - 1);
      }
      if (y != x) cov[getsg(y)] = true;
    }
    int res = 0;
    while (cov[res]) res++;
    sg[x] = res;
    return res;
  }
}
void init() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  sg[0] = 0;
}
void solve() {
  int ans = 0;
  for (int i = 1; i <= n; i++) {
    for (int j = 2; j * j <= a[i]; j++) {
      if (a[i] % j == 0) {
        int v = 0;
        for (int k = 1; k <= n; k++) {
          int cnt = -1;
          while (a[k] % j == 0) {
            a[k] /= j;
            cnt++;
          }
          if (cnt >= 0) v |= 1 << cnt;
        }
        ans ^= getsg(v);
      }
    }
    if (a[i] > 1) {
      int j = a[i];
      int v = 0;
      for (int k = 1; k <= n; k++) {
        int cnt = -1;
        while (a[k] % j == 0) {
          a[k] /= j;
          cnt++;
        }
        if (cnt >= 0) v |= 1 << cnt;
      }
      ans ^= getsg(v);
    }
  }
  if (ans)
    printf("Mojtaba\n");
  else
    printf("Arpa\n");
}
int main() {
  init();
  solve();
}
