850_C. Arpa and a game with Mojtaba
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.
```python
import sys
input = sys.stdin.buffer.readline
from collections import Counter

games = Counter() # prime : bitmask of if that power of the prime exists

def add_primes(a):
    i = 2
    while i*i <= a:
        cnt = 0
        while a % i == 0:
            a //= i
            cnt += 1

        if cnt:
            games[i] |= 1 << cnt

        i += 1

    if a != 1:
        games[a] |= 1 << 1

def mex(a):
    i = 0
    while True:
        if i not in a:
            return i
        i += 1

grundy_val = {}
def grundy_value(mask):
    if mask in grundy_val:
        return grundy_val[mask]
    else:
        transition_masks = set()
        k = 1
        while 1<<k <= mask:
            new_mask = (mask&((1<<k)-1))|(mask>>k)
            transition_masks.add(grundy_value(new_mask))
            k += 1

        grundy_val[mask] = mex(transition_masks)
        return grundy_val[mask]


n = int(input())
a = list(map(int,input().split()))

for i in a:
    add_primes(i)

xor_sum = 0
for game in games.values():
    grundy_val = {}
    xor_sum ^= grundy_value(game)

if xor_sum:
    print("Mojtaba")
else:
    print("Arpa")
```