#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 7;
int fx[] = {-1, +0, +1, +0, +1, +1, -1, -1, +0};
int fy[] = {+0, -1, +0, +1, +1, -1, +1, -1, +0};
int day[] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
template <typename T>
inline bool isLeap(T y) {
  return (y % 400 == 0) || (y % 100 ? y % 4 == 0 : false);
}
template <typename T>
inline T GCD(T a, T b) {
  a = abs(a);
  b = abs(b);
  if (a < b) swap(a, b);
  while (b) {
    a = a % b;
    swap(a, b);
  }
  return a;
}
template <typename T>
inline T EGCD(T a, T b, T &x, T &y) {
  if (a == 0) {
    x = 0;
    y = 1;
    return b;
  }
  T x1, y1;
  T d = EGCD(b % a, a, x1, y1);
  x = y1 - (b / a) * x1;
  y = x1;
  return d;
}
template <typename T>
inline T LCM(T x, T y) {
  T tp = GCD(x, y);
  if ((x / tp) * 1. * y > 9e18) return 9e18;
  return (x / tp) * y;
}
template <typename T>
inline T BigMod(T A, T B, T M = MOD) {
  T ret = 1;
  while (B) {
    if (B & 1) ret = (ret * A) % M;
    A = (A * A) % M;
    B = B >> 1;
  }
  return ret;
}
template <typename T>
inline T InvMod(T A, T M = MOD) {
  return BigMod(A, M - 2, M);
}
template <typename T>
T scani(T &n) {
  n = 0;
  bool negative = false;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') negative = true;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    n = n * 10 + c - 48;
    c = getchar();
  }
  if (negative) n = ~(n - 1);
  return n;
}
template <typename T>
void write(T n, int type = true) {
  if (n < 0) {
    putchar('-');
    n = -n;
  }
  if (!n) {
    putchar('0');
    if (type == 32)
      putchar(' ');
    else if (type)
      putchar('\n');
    return;
  }
  char buff[22];
  int len = 0;
  while (n) buff[len++] = n % 10 + 48, n /= 10;
  for (int i = len - 1; i >= 0; i--) putchar(buff[i]);
  if (type == 32)
    putchar(' ');
  else if (type)
    putchar('\n');
}
int scans(char *a) {
  int i = 0;
  char c = 0;
  while (c < 33) c = getchar();
  while (c > 33) {
    a[i++] = c;
    c = getchar();
  }
  a[i] = 0;
  return i;
}
template <typename T>
inline T SqrDis(T x1, T y1, T x2, T y2) {
  return ((x1 - x2) * (x1 - x2)) + ((y1 - y2) * (y1 - y2));
}
template <typename T>
inline T Area2(T Ax, T Ay, T Bx, T By, T Cx, T Cy) {
  T ret = Ax * (By - Cy) + Bx * (Cy - Ay) + Cx * (Ay - By);
  if (ret < 0) return ret = -ret;
  return ret;
}
const int N = 2000006;
const int M = 44444;
const unsigned long long hs = 3797;
unordered_map<int, int> dp;
unordered_set<int> prime;
int in[N], n;
int ans_me(int mask) {
  if (dp.find(mask) != dp.end()) return dp[mask];
  unordered_set<int> vs;
  for (int i = 0; mask >> i; i++) {
    int newMask = (mask >> (i + 1)) | (mask & ((1 << i) - 1));
    vs.insert(ans_me(newMask));
  }
  int ret = 0;
  while (vs.find(ret) != vs.end()) ret++;
  return dp[mask] = ret;
}
int main() {
  scani(n);
  for (int i = (0); i < (n); ++i) {
    int x = scani(in[i]);
    for (int i = 2; i * 1LL * i <= x; i++) {
      if (x % i == 0) {
        prime.insert(i);
        while (x % i == 0) x /= i;
      }
    }
    if (x > 1) prime.insert(x);
  }
  int win = 0;
  for (auto p : prime) {
    int mask = 0;
    for (int i = (0); i < (n); ++i) {
      int cnt = 0;
      while (in[i] % p == 0) {
        in[i] /= p;
        cnt++;
      }
      if (cnt) mask |= (1 << (cnt - 1));
    }
    win ^= ans_me(mask);
  }
  puts(win ? "Mojtaba" : "Arpa");
  return 0;
}

### Prompt

Your challenge is to write a CPP solution to the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 7;
int fx[] = {-1, +0, +1, +0, +1, +1, -1, -1, +0};
int fy[] = {+0, -1, +0, +1, +1, -1, +1, -1, +0};
int day[] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
template <typename T>
inline bool isLeap(T y) {
  return (y % 400 == 0) || (y % 100 ? y % 4 == 0 : false);
}
template <typename T>
inline T GCD(T a, T b) {
  a = abs(a);
  b = abs(b);
  if (a < b) swap(a, b);
  while (b) {
    a = a % b;
    swap(a, b);
  }
  return a;
}
template <typename T>
inline T EGCD(T a, T b, T &x, T &y) {
  if (a == 0) {
    x = 0;
    y = 1;
    return b;
  }
  T x1, y1;
  T d = EGCD(b % a, a, x1, y1);
  x = y1 - (b / a) * x1;
  y = x1;
  return d;
}
template <typename T>
inline T LCM(T x, T y) {
  T tp = GCD(x, y);
  if ((x / tp) * 1. * y > 9e18) return 9e18;
  return (x / tp) * y;
}
template <typename T>
inline T BigMod(T A, T B, T M = MOD) {
  T ret = 1;
  while (B) {
    if (B & 1) ret = (ret * A) % M;
    A = (A * A) % M;
    B = B >> 1;
  }
  return ret;
}
template <typename T>
inline T InvMod(T A, T M = MOD) {
  return BigMod(A, M - 2, M);
}
template <typename T>
T scani(T &n) {
  n = 0;
  bool negative = false;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') negative = true;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    n = n * 10 + c - 48;
    c = getchar();
  }
  if (negative) n = ~(n - 1);
  return n;
}
template <typename T>
void write(T n, int type = true) {
  if (n < 0) {
    putchar('-');
    n = -n;
  }
  if (!n) {
    putchar('0');
    if (type == 32)
      putchar(' ');
    else if (type)
      putchar('\n');
    return;
  }
  char buff[22];
  int len = 0;
  while (n) buff[len++] = n % 10 + 48, n /= 10;
  for (int i = len - 1; i >= 0; i--) putchar(buff[i]);
  if (type == 32)
    putchar(' ');
  else if (type)
    putchar('\n');
}
int scans(char *a) {
  int i = 0;
  char c = 0;
  while (c < 33) c = getchar();
  while (c > 33) {
    a[i++] = c;
    c = getchar();
  }
  a[i] = 0;
  return i;
}
template <typename T>
inline T SqrDis(T x1, T y1, T x2, T y2) {
  return ((x1 - x2) * (x1 - x2)) + ((y1 - y2) * (y1 - y2));
}
template <typename T>
inline T Area2(T Ax, T Ay, T Bx, T By, T Cx, T Cy) {
  T ret = Ax * (By - Cy) + Bx * (Cy - Ay) + Cx * (Ay - By);
  if (ret < 0) return ret = -ret;
  return ret;
}
const int N = 2000006;
const int M = 44444;
const unsigned long long hs = 3797;
unordered_map<int, int> dp;
unordered_set<int> prime;
int in[N], n;
int ans_me(int mask) {
  if (dp.find(mask) != dp.end()) return dp[mask];
  unordered_set<int> vs;
  for (int i = 0; mask >> i; i++) {
    int newMask = (mask >> (i + 1)) | (mask & ((1 << i) - 1));
    vs.insert(ans_me(newMask));
  }
  int ret = 0;
  while (vs.find(ret) != vs.end()) ret++;
  return dp[mask] = ret;
}
int main() {
  scani(n);
  for (int i = (0); i < (n); ++i) {
    int x = scani(in[i]);
    for (int i = 2; i * 1LL * i <= x; i++) {
      if (x % i == 0) {
        prime.insert(i);
        while (x % i == 0) x /= i;
      }
    }
    if (x > 1) prime.insert(x);
  }
  int win = 0;
  for (auto p : prime) {
    int mask = 0;
    for (int i = (0); i < (n); ++i) {
      int cnt = 0;
      while (in[i] % p == 0) {
        in[i] /= p;
        cnt++;
      }
      if (cnt) mask |= (1 << (cnt - 1));
    }
    win ^= ans_me(mask);
  }
  puts(win ? "Mojtaba" : "Arpa");
  return 0;
}

```