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;
bool check(int n, int pos) { return (n & (1 << pos)) >> pos; }
int on(int n, int pos) { return n | (1 << pos); }
int off(int n, int pos) { return n & ~(1 << pos); }
const int M = 400010, mod = 1000000007;
map<int, int> dp;
int call(int mask) {
  if (mask == 0) return 0;
  if (dp.find(mask) != dp.end()) return dp[mask];
  set<int> mex;
  for (int i = 1; i <= 32 - __builtin_clz(mask); i++) {
    int low = mask & ((1 << (i - 1)) - 1);
    int high = mask >> i;
    mex.insert(call(low | high));
  }
  int ans = 0;
  for (int a : mex) {
    if (a != ans) return dp[mask] = ans;
    ans++;
  }
  return dp[mask] = ans;
}
map<int, int> pmask;
int main() {
  ios_base::sync_with_stdio(false);
  int n, i, j, k, num;
  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", &num);
    if (num == 1) continue;
    for (j = 2; j * j <= num; j++) {
      int cnt = 0;
      while (num % j == 0) num /= j, cnt++;
      if (cnt) {
        pmask[j] = pmask[j] | on(0, cnt - 1);
      }
    }
    if (num > 1) {
      pmask[num] = pmask[num] | on(0, 0);
    }
  }
  int sum = 0;
  for (auto a : pmask) sum ^= call(a.second);
  if (sum == 0)
    printf("Arpa\n");
  else
    printf("Mojtaba\n");
  return 0;
}
