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;
int n;
map<int, vector<int> > game;
map<int, int> vis;
int dfs(int mask) {
  if (mask == 0) return 0;
  if (vis.count(mask)) return vis[mask];
  set<int> S;
  int top = 1;
  while ((1 << top) <= mask) ++top;
  for (int j = 0; j < top; ++j) {
    int nmask = 0;
    for (int k = 0; k < (j); ++k)
      if (mask >> k & 1) nmask |= 1 << k;
    for (int k = j; k < (top); ++k)
      if (mask >> k & 1 && (k > j)) nmask |= 1 << (k - (j + 1));
    S.insert(dfs(nmask));
  }
  int& res = vis[mask];
  while (S.count(res)) ++res;
  return res;
}
int SG(vector<int> v) {
  int mask = 0;
  for (auto e : v) mask |= 1 << (e - 1);
  return dfs(mask);
}
int sg[100];
void test() {
  sg[0] = 0;
  for (int i = 1; i < (100); ++i) {
    set<int> S;
    int top = 1;
    while ((1 << top) <= i) ++top;
    for (int j = 0; j < top; ++j) {
      int nmask = 0;
      for (int k = 0; k < (j); ++k)
        if (i >> k & 1) nmask |= 1 << k;
      for (int k = j; k < (top); ++k)
        if (i >> k & 1 && (k > j)) nmask |= 1 << (k - (j + 1));
      S.insert(sg[nmask]);
    }
    int& res = sg[i];
    while (S.count(res)) ++res;
    cout << i << " " << res << endl;
  }
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < (n); ++i) {
    int x;
    scanf("%d", &x);
    for (int t = 2; t * t <= x; ++t)
      if (x % t == 0) {
        int times = 0;
        while (x % t == 0) times++, x /= t;
        game[t].push_back(times);
      }
    if (x > 1) game[x].push_back(1);
  }
  int sg = 0;
  for (auto e : game) sg ^= SG(e.second);
  puts(sg ? "Mojtaba" : "Arpa");
  return 0;
}
