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>
#pragma comment(linker, "/STACK:336777216")
using namespace std;
const int MAXN = 100 + 10;
int N;
int a[MAXN];
map<int, long long> Map;
map<long long, int> SG;
int CalcSG(long long i) {
  if (i == 0) return 0;
  if (SG.find(i) != SG.end()) return SG[i];
  int Used[35];
  memset(Used, 0, sizeof(Used));
  for (int k = 1; k < 35; k++) {
    if (i >> (k - 1)) {
      int ne = (i >> k) | (i & ((1LL << (k - 1)) - 1));
      Used[CalcSG(ne)] = 1;
    }
  }
  int sg = 0;
  while (Used[sg]) sg++;
  return SG[i] = sg;
}
void Work() {
  scanf("%d", &N);
  for (int i = 0; i < N; i++) {
    scanf("%d", &a[i]);
    int pnt = a[i];
    for (int p = 2; p * p <= a[i]; p++) {
      int POW = 0;
      while (pnt % p == 0) {
        pnt /= p;
        POW++;
      }
      if (POW) Map[p] = Map[p] | (1LL << (POW - 1));
    }
    if (pnt != 1) Map[pnt] = Map[pnt] | 1;
  }
  int Ans = 0;
  for (auto it : Map) Ans ^= CalcSG(it.second);
  printf(Ans ? "Mojtaba\n" : "Arpa\n");
}
int main() {
  Work();
  return 0;
}
