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;
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
int n, sg[1 << 20], a[105], stat[100005], ans = 0, now = 0, at[1000000];
map<int, int> vis, res, mp;
int Calc(int x) {
  if (vis[x]) return res[x];
  vis[x] = 1;
  for (int i = 1; 1 << i - 1 <= x; ++i) {
    int st = x & ((1 << i - 1) - 1) | (x >> i);
    Calc(st);
  }
  ++now;
  int r = 0;
  for (int i = 1; 1 << i - 1 <= x; ++i) {
    int st = x & ((1 << i - 1) - 1) | (x >> i);
    at[Calc(st)] = now;
  }
  for (; at[r] == now; ++r)
    ;
  return res[x] = r;
}
int main() {
  n = read();
  mp[1] = 1;
  for (int i = 1; i <= n; ++i) {
    a[i] = read();
    for (int j = 2; j <= 100000; ++j)
      if (a[i] % j == 0) {
        int k = 0;
        do ++k, a[i] /= j;
        while (a[i] % j == 0);
        stat[j] |= 1 << k - 1;
      }
    if (!mp[a[i]]) ans ^= 1, mp[a[i]] = 1;
  }
  sg[0] = 0;
  for (int x = 1; x < 1 << 19; ++x) {
    ++now;
    sg[x] = 0;
    for (int i = 1; 1 << i - 1 <= x; ++i) {
      int st = x & ((1 << i - 1) - 1) | (x >> i);
      at[sg[st]] = now;
    }
    for (; at[sg[x]] == now; ++sg[x])
      ;
  }
  for (int i = 1; i <= 100000; ++i)
    if (stat[i] < 1 << 19)
      ans ^= sg[stat[i]];
    else
      ans ^= Calc(stat[i]);
  puts(ans ? "Mojtaba" : "Arpa");
  return 0;
}
