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 long long INF = 0x3f3f3f3f;
const int N = 1e5 + 10;
const long long mod = 1e9 + 7;
const double e = 1e-10;
const double PI = acos(-1);
int cnt[N];
int prime[N];
bool check[N];
map<int, pair<int, int> > sg;
int get_sg(int x) {
  if (!x) return 0;
  if (sg[x].first) return sg[x].second;
  int v = 0, s[50];
  memset(s, 0, sizeof(s));
  for (int i = 0; i <= 31; ++i) {
    if (x == v) break;
    if (!sg[(x >> (i + 1)) | v].first) get_sg((x >> (i + 1)) | v);
    s[sg[(x >> (i + 1)) | v].second]++;
    v |= (((x >> i) & 1) << i);
  }
  int now = 0;
  while (s[now]) now++;
  sg[x].first = 1;
  return sg[x].second = now;
}
int main() {
  memset(check, false, sizeof(check));
  int tot = 0;
  for (int i = 2; i <= N; ++i) {
    if (!check[i]) prime[++tot] = i;
    for (int j = 1; j <= tot; ++j) {
      if (i * prime[j] > N) break;
      check[i * prime[j]] = true;
      if (i % prime[j] == 0) break;
    }
  }
  int n, x, k;
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &x);
    for (int now = 1; now <= tot; now++) {
      if (prime[now] > x) continue;
      k = 0;
      while (x % prime[now] == 0) {
        k++;
        x /= prime[now];
      }
      if (k) cnt[now] |= (1 << (k - 1));
    }
    if (x != 1) prime[++tot] = x, cnt[tot] = 1;
  }
  int ans = 0;
  for (int i = 1; i <= tot; ++i) {
    if (!sg[cnt[i]].first) get_sg(cnt[i]);
    ans ^= sg[cnt[i]].second;
  }
  if (ans)
    puts("Mojtaba");
  else
    puts("Arpa");
  return 0;
}
