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;
const int GR = 31, INF = (int)2e9, M = (int)1e5;
int pot[GR];
int n, xoro;
bool f[M + 5];
map<int, int> nim, maska;
int mex(vector<int> &q) {
  if (q.empty()) return 0;
  sort(q.begin(), q.end());
  if (q[0] != 0) return 0;
  for (int i = 1; i < q.size(); i++) {
    while (q[i] == q[i - 1]) i++;
    if (q[i] != q[i - 1] + 1) return q[i - 1] + 1;
  }
  return q.back() + 1;
}
void zrob(int a) {
  if (a == 1) {
    nim[1] = 0;
    return;
  }
  vector<int> q;
  int nowa = 0;
  for (int i = 0; i < GR; i++) {
    int x = a >> (i + 1);
    if (a & pot[i]) nowa += pot[i];
    x |= nowa;
    if (nim.find(x) == nim.end()) {
      nim[x] = INF;
      zrob(x);
    }
    q.push_back(nim[x]);
  }
  nim[a] = mex(q);
}
void dodaj(int &y, int j) {
  int ile = 0;
  while (y % j == 0) {
    ile++;
    y /= j;
  }
  if (maska.find(j) == maska.end()) maska[j] = 0;
  maska[j] |= pot[ile];
}
int main() {
  pot[0] = 1;
  for (int i = 1; i < GR; i++) pot[i] = 2 * pot[i - 1];
  for (int i = 2; i * i <= M; i++)
    if (!f[i])
      for (int j = i * i; j <= M; j += i) f[j] = true;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    int x, y;
    scanf("%d", &x);
    y = x;
    for (int j = 2; j * j <= x; j++)
      if (x % j == 0 and !f[j]) dodaj(y, j);
    if (y > 1) dodaj(y, y);
  }
  for (auto it = maska.begin(); it != maska.end(); it++) {
    int start = it->second;
    nim[start] = INF;
    zrob(start);
    xoro ^= nim[start];
    nim.clear();
  }
  if (xoro == 0)
    printf("Arpa");
  else
    printf("Mojtaba");
}
