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 = 1e5;
int n;
bool flag[MaxN + 5];
int tot, prime[MaxN + 5];
map<int, int> SG, num;
int Get_SG(int x) {
  if (x == 0) return 0;
  if (SG.count(x)) return SG[x];
  map<int, int> vis;
  int temp = x, cnt = 0;
  while (temp) temp /= 2, cnt++;
  for (int i = 1; i <= cnt; i++)
    vis[Get_SG((x >> i) | (x & ((1 << i - 1) - 1)))] = 1;
  for (int i = 0;; i++)
    if (!vis[i]) return SG[x] = i;
}
void Get_Prime() {
  memset(flag, 0, sizeof(flag));
  flag[1] = 1;
  tot = 0;
  for (int i = 2; i <= MaxN; i++) {
    if (flag[i] == 0) prime[++tot] = i;
    for (int j = 1; j <= tot; j++) {
      if (prime[j] * i > MaxN) break;
      flag[prime[j] * i] = 1;
      if (i % prime[j] == 0) break;
    }
  }
}
void Solve(int x) {
  for (int i = 1; prime[i] * prime[i] <= x; i++) {
    int cnt = 0;
    while (x % prime[i] == 0) {
      x /= prime[i];
      cnt++;
    }
    if (cnt) num[prime[i]] = num[prime[i]] | 1 << (cnt - 1);
  }
  if (x != 1) num[x] = num[x] | 1;
}
int main() {
  Get_Prime();
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    int x;
    scanf("%d", &x);
    Solve(x);
  }
  map<int, int>::iterator it;
  int ok = 0;
  for (it = num.begin(); it != num.end(); it++) ok ^= Get_SG(it->second);
  if (ok)
    printf("Mojtaba\n");
  else
    printf("Arpa\n");
}
