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 INF = 1e9 + 5;
const int MAXN = 100007;
const int MOD = 30021;
const double eps = 1e-8;
const double PI = acos(-1.0);
map<int, int> SG, num;
int getSG(int x) {
  if (x == 0) return 0;
  if (SG.count(x)) return SG[x];
  map<int, int> vis;
  int p = x;
  int t = 0;
  while (p) p /= 2, t++;
  for (int k = 1; k <= t; k++)
    vis[getSG((x >> k) | (x & ((1 << k - 1) - 1)))] = 1;
  for (int i = 0;; i++)
    if (!vis[i]) return SG[x] = i;
}
int prime[MAXN], primesize;
bool isprime[MAXN];
void getlist(int listsize) {
  memset(isprime, 1, sizeof(isprime));
  isprime[1] = false;
  for (int i = 2; i <= listsize; i++) {
    if (isprime[i]) prime[++primesize] = i;
    for (int j = 1; j <= primesize && i * prime[j] <= listsize; j++) {
      isprime[i * prime[j]] = false;
      if (i % prime[j] == 0) break;
    }
  }
}
void solve() {
  int t, x;
  scanf("%d", &x);
  for (int i = 1; prime[i] * prime[i] <= x; i++) {
    t = 0;
    while (x % prime[i] == 0) x /= prime[i], t++;
    if (t != 0) num[prime[i]] = num[prime[i]] | 1 << (t - 1);
  }
  if (x != 1) num[x] = num[x] | 1;
}
int main() {
  getlist(100005);
  int n;
  int x;
  int ans = 0;
  scanf("%d", &n);
  while (n--) solve();
  map<int, int>::iterator it;
  for (it = num.begin(); it != num.end(); it++) ans ^= getSG(it->second);
  if (ans == 0)
    printf("Arpa\n");
  else
    printf("Mojtaba\n");
}
