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;
long long int x, y;
long long int gcd(long long int a, long long int b) {
  if (a == 0) {
    x = 0, y = 1;
    return b;
  }
  long long int gc = gcd(b % a, a);
  long long int temp;
  temp = x;
  x = y - (b / a) * temp;
  y = temp;
  return gc;
}
long long int pow(long long int a, long long int x, long long int m) {
  long long int ans = 1, k = 1;
  while (k <= x) {
    if (x % k) ans = ((ans * a) % m);
    k <<= 1;
    a *= a;
    a %= m;
  }
  return ans;
}
vector<int> prime;
int second[100005];
void sieve() {
  int i, j;
  prime.push_back(2);
  for (i = 3; i < 100005; i += 2) {
    if (second[i] != -1) {
      prime.push_back(i);
      for (j = i; i * 1LL * j < 100005; j += 2) {
        second[i * j] = -1;
      }
    }
  }
}
int a[100005];
map<int, set<int> > fact;
int lb(int n) {
  int i;
  for (i = 0; i < 31; i++) {
    if (n < (1 << i)) {
      return i;
    }
  }
  return i;
}
unordered_map<int, int> va;
unordered_map<int, int> mark;
int solve(int val) {
  if (mark[val] == 1) {
    return va[val];
  }
  if (val == 0) return 0;
  int k = lb(val);
  set<int> temp;
  for (int i = 1; i <= k; i++) {
    int a = val >> i;
    int b = val & ((1 << (i - 1)) - 1);
    temp.insert(solve(a | b));
  }
  k = 0;
  for (auto i : temp) {
    if (i != k) {
      va[val] = k;
      mark[val] = 1;
      return k;
    }
    k++;
  }
  mark[val] = 1;
  va[val] = k;
  return k;
}
int main() {
  ios::sync_with_stdio(false);
  cout.tie(0);
  cin.tie(0);
  int n;
  cin >> n;
  sieve();
  int i, j;
  for (i = 0; i < n; i++) {
    cin >> a[i];
    j = a[i];
    int cn;
    for (auto k : prime) {
      cn = 0;
      while (j % k == 0) {
        j /= k;
        cn++;
      }
      if (cn > 0) fact[k].insert(cn);
    }
    if (j != 1) fact[j].insert(1);
  }
  int cur;
  int ans = 0;
  for (auto k : fact) {
    cur = 0;
    for (auto t : k.second) {
      cur |= (1 << (t - 1));
    }
    ans ^= solve(cur);
  }
  if (ans)
    cout << "Mojtaba";
  else
    cout << "Arpa";
}
