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 mod = 1e9 + 7;
const double PI = acos(-1);
const double EPS = 1e-6;
const int INF = 0x3f3f3f3f;
inline int readint() {
  int sum = 0;
  char c = getchar();
  bool f = 0;
  while (c < '0' || c > '9') {
    if (c == '-') f = 1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    sum = sum * 10 + c - '0';
    c = getchar();
  }
  if (f) return -sum;
  return sum;
}
inline long long readLL() {
  long long sum = 0;
  char c = getchar();
  bool f = 0;
  while (c < '0' || c > '9') {
    if (c == '-') f = 1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    sum = sum * 10 + c - '0';
    c = getchar();
  }
  if (f) return -sum;
  return sum;
}
map<int, int> ss;
map<int, int> s;
map<int, set<int> > megumi;
int getSG(int n) {
  if (!n) return 0;
  if (ss.count(n)) return ss[n];
  for (int i = 0; (1 << i) <= n; i++)
    megumi[n].insert(getSG((n >> (i + 1)) | (n & ((1 << i) - 1))));
  for (int j = 0;; j++) {
    if (!megumi[n].count(j)) {
      return ss[n] = j;
    }
  }
}
int main() {
  int n = readint();
  for (int i = 1; i <= n; i++) {
    int x = readint();
    for (int i = 2; i <= int(sqrt(x) + 0.5); i++) {
      if (x % i == 0) {
        int cnt = 0;
        while (x % i == 0) {
          x /= i;
          cnt++;
        }
        s[i] |= 1 << (cnt - 1);
      }
    }
    if (x > 1) s[x] |= 1 << (0);
  }
  int ans = 0;
  map<int, int>::iterator it;
  for (it = s.begin(); it != s.end(); it++) {
    ans ^= getSG(it->second);
  }
  if (ans == 0)
    printf("Arpa\n");
  else
    printf("Mojtaba\n");
  return 0;
}
