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;
inline int read() {
  int x = 0, flag = 1;
  char c;
  while ((c = getchar()) < '0' || c > '9')
    if (c == '-') flag = -1;
  while (c >= '0' && c <= '9')
    x = (x << 3) + (x << 1) + (c ^ 48), c = getchar();
  return x * flag;
}
map<int, int> st, sg;
void fuck(int x) {
  for (int i = 2; i * i <= x; i++) {
    int t = 0;
    while (x % i == 0) {
      t++;
      x /= i;
    }
    if (t) st[i] |= 1 << (t - 1);
  }
  if (x > 1) st[x] |= 1;
}
int get(int x) {
  if (x == 0) return 0;
  if (sg.count(x)) return sg[x];
  map<int, int> vis;
  int p = x, k = 0;
  while (p) p >>= 1, k++;
  for (int i = 1; i <= k; i++)
    vis[get((x >> i) | (x & ((1 << i - 1) - 1)))] = 1;
  for (int i = 0;; i++)
    if (!vis[i]) return sg[x] = i;
}
int main() {
  int n = read(), flag = 0;
  for (int i = 1; i <= n; i++) fuck(read());
  map<int, int>::iterator it = st.begin();
  for (; it != st.end(); it++) flag ^= get(it->second);
  if (flag)
    puts("Mojtaba");
  else
    puts("Arpa");
}
