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;
template <class T>
T power(T N, T P) {
  return (P == 0) ? 1 : N * power(N, P - 1);
}
template <class T>
T gcd(T a, T b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
struct debugger {
  template <typename T>
  debugger& operator,(const T& v) {
    cerr << v << " ";
    return *this;
  }
} dbg;
void make_unique(vector<int>& a) {
  sort(a.begin(), a.end());
  a.erase(unique(a.begin(), a.end()), a.end());
}
long long int bigmod(long long int B, long long int P, long long int M) {
  long long int R = 1;
  while (P > 0) {
    if (P % 2 == 1) {
      R = (R * B) % M;
    }
    P /= 2;
    B = (B * B) % M;
  }
  return R;
}
int on(int n, int pos) { return n = n | (1 << pos); }
void off(int& n, int pos) { n = n & ~(1 << pos); }
bool check(int n, int pos) { return (bool)(n & (1 << pos)); }
const int N = (int)1e6 + 10;
const int MX = 1e5;
map<int, int> mp;
map<int, int>::iterator it;
map<int, int> dp;
map<int, bool> vis;
void cal(int v) {
  int x = v;
  for (int i = 2; i < MX; i++) {
    int cnt = 0;
    if (x % i == 0) {
      while (x % i == 0) {
        ++cnt;
        x /= i;
      }
      mp[i] = on(mp[i], cnt - 1);
    }
  }
  if (x > 1) {
    mp[x] = on(mp[x], 0);
  }
}
int rec(int mask) {
  if (mask == 0) return 0;
  if (vis[mask]) return dp[mask];
  vis[mask] = true;
  int arr[100];
  memset(arr, 0, sizeof(arr));
  for (int i = 0; i < 31; i++) {
    if ((1 << i) > mask) break;
    int nxt = ((mask >> (i + 1)) | (mask & ((1 << i) - 1)));
    int g = rec(nxt);
    arr[g] = 1;
  }
  for (int i = 0; i < 100; i++) {
    if (arr[i] == 0) {
      return dp[mask] = i;
    }
  }
}
int main() {
  int n, x;
  while (scanf("%d", &n) != EOF) {
    mp.clear();
    vis.clear();
    dp.clear();
    for (int i = 0; i < n; i++) {
      scanf("%d", &x);
      cal(x);
    }
    int tot = 0, xr = 0;
    for (it = mp.begin(); it != mp.end(); it++) {
      xr ^= rec(it->second);
    }
    printf("%s\n", xr ? "Mojtaba" : "Arpa");
  }
  return 0;
}
