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 double eps = 1e-10;
int read() {
  char ch = getchar();
  int f = 0;
  while (ch < '0' || ch > '9') ch = getchar();
  while (ch >= '0' && ch <= '9') {
    f = f * 10 + (ch ^ 48);
    ch = getchar();
  }
  return f;
}
int n, a[105], s[1000005], head;
map<int, int> mp;
int sqr(int x) { return x * x; }
int get_sg(int x, int maxx) {
  if (mp.find(x) != mp.end()) return mp[x];
  while (maxx && (x & (1 << (maxx - 1))) == 0) maxx--;
  if (!maxx) return maxx;
  bool vis[30] = {0};
  for (int i = 1; i <= maxx; i++) {
    int now = x >> i;
    now |= x & ((1 << (i - 1)) - 1);
    vis[get_sg(now, max(maxx - i, i - 1))] = 1;
  }
  for (int i = 0;; i++)
    if (!vis[i]) return mp[x] = i;
}
int ans;
void fuck(int x) {
  int t = 0, maxx = 0;
  for (int i = 1; i <= n; i++) {
    int temp = a[i], temp2 = 0;
    while (!(temp % x)) {
      temp /= x, temp2++;
    }
    if (temp2) t |= 1 << (temp2 - 1);
    maxx = max(maxx, temp2);
  }
  ans ^= get_sg(t, maxx);
}
int main() {
  n = read();
  for (int i = 1; i <= n; i++) {
    a[i] = read();
    int x = a[i], x1 = x;
    for (int j = 2; sqr(j) <= x1; j++) {
      if (!(x % j)) {
        s[++head] = j;
        while (!(x % j)) x /= j;
      }
    }
    if (x > 1) s[++head] = x;
  }
  sort(s + 1, s + head + 1);
  for (int i = 1; i <= head; i++) {
    if (s[i] != s[i - 1]) fuck(s[i]);
  }
  if (!ans)
    puts("Arpa");
  else
    puts("Mojtaba");
  return 0;
}
