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 read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch - '0' < 0 || ch - '0' > 9) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch - '0' >= 0 && ch - '0' <= 9) {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
int n;
int a[105];
int fac[105 * 10], top;
int ans;
map<int, int> sg;
int SG(int S) {
  if (sg.count(S)) return sg[S];
  int book[32] = {0};
  for (int i = 0; (1 << i) <= S; i++) {
    int tmp = ((S >> (i + 1)) | (S & ((1 << i) - 1)));
    book[SG(tmp)] = 1;
  }
  for (int i = 0;; i++) {
    if (!book[i]) {
      sg[S] = i;
      break;
    }
  }
  return sg[S];
}
int solve(int x) {
  int all = 0;
  for (int i = 1; i <= n; i++) {
    int tmp = a[i], ci = 0;
    while (tmp % x == 0) tmp /= x, ci++;
    if (ci) all |= (1 << (ci - 1));
  }
  return SG(all);
}
int main() {
  n = read();
  for (int i = 1; i <= n; i++) {
    a[i] = read();
    int tmp = a[i];
    for (int j = 2; j <= sqrt(a[i]); j++) {
      if (tmp % j == 0) {
        fac[++top] = j;
        while (tmp % j == 0) tmp /= j;
      }
    }
    if (tmp != 1) fac[++top] = tmp;
  }
  sort(fac + 1, fac + top + 1);
  top = unique(fac + 1, fac + top + 1) - fac - 1;
  for (int i = 1; i <= top; i++) ans ^= solve(fac[i]);
  if (!ans)
    puts("Arpa");
  else
    puts("Mojtaba");
  return 0;
}
