#include <bits/stdc++.h>
int clock0 = clock();
using namespace std;
template <class _T>
inline _T sqr(const _T &first) {
  return first * first;
}
template <class _T>
inline string tostr(const _T &a) {
  ostringstream os("");
  os << a;
  return os.str();
}
const long double PI = 3.1415926535897932384626433832795L;
const long double EPS = 1e-9;
char TEMPORARY_CHAR;
const int INF = 2e9;
inline void fft(vector<complex<long double> > &a, bool invert) {
  int n = (int)a.size();
  for (int i = 1, j = 0; i < n; ++i) {
    int bit = n >> 1;
    for (; j >= bit; bit >>= 1) j -= bit;
    j += bit;
    if (i < j) swap(a[i], a[j]);
  }
  for (int len = 2; len <= n; len <<= 1) {
    long double ang = 2 * PI / len * (invert ? -1 : 1);
    complex<long double> wlen(cos(ang), sin(ang));
    for (int i = 0; i < n; i += len) {
      complex<long double> w(1);
      for (int j = 0; j < len / 2; ++j) {
        complex<long double> u = a[i + j], v = a[i + j + len / 2] * w;
        a[i + j] = u + v;
        a[i + j + len / 2] = u - v;
        w *= wlen;
      }
    }
  }
  if (invert)
    for (int i = 0; i < n; ++i) a[i] /= n;
}
inline void input(int &a) {
  a = 0;
  while (((TEMPORARY_CHAR = getchar()) > '9' || TEMPORARY_CHAR < '0') &&
         (TEMPORARY_CHAR != '-')) {
  }
  char neg = 0;
  if (TEMPORARY_CHAR == '-') {
    neg = 1;
    TEMPORARY_CHAR = getchar();
  }
  while (TEMPORARY_CHAR <= '9' && TEMPORARY_CHAR >= '0') {
    a = (a << 3) + (a << 1) + TEMPORARY_CHAR - '0';
    TEMPORARY_CHAR = getchar();
  }
  if (neg) a = -a;
}
inline void out(int a) {
  if (!a) putchar('0');
  if (a < 0) {
    putchar('-');
    a = -a;
  }
  char s[10];
  int i;
  for (i = 0; a; ++i) {
    s[i] = '0' + a % 10;
    a /= 10;
  }
  for (int j = (i)-1; j >= 0; j--) putchar(s[j]);
}
inline int nxt() {
  int(ret);
  input((ret));
  ;
  return ret;
}
struct lnum {
  vector<int> a;
  int base;
  lnum(int num = 0, int base = 1000000000) : base(base) {
    if (!num) a.resize(1);
    while (num) {
      a.push_back(num % base);
      num /= base;
    }
  }
  inline int len() const { return a.size(); }
  lnum &operator=(const lnum &l) {
    if (this != &l) {
      a = l.a;
      base = l.base;
    }
    return *this;
  }
  inline friend lnum operator+(const lnum &l, const lnum &r) {
    lnum ret(0, l.base);
    int base = l.base;
    int ln = l.len(), rn = r.len();
    int n = max(ln, rn);
    ret.a.resize(n);
    int o = 0;
    for (int i = 0; i < n; ++i) {
      int s = o;
      if (i < ln) s += l.a[i];
      if (i < rn) s += r.a[i];
      o = s >= base;
      if (o) s -= base;
      ret.a[i] = s;
    }
    if (o) ret.a.push_back(1);
    return ret;
  }
  inline friend lnum operator-(const lnum &l, const lnum &r) {
    lnum ret(0, l.base);
    int base = l.base;
    int n = l.len();
    int rn = r.len();
    ret.a.resize(n);
    int o = 0;
    for (int i = 0; i < n; ++i) {
      int s = l.a[i] - o;
      if (i < rn) s -= r.a[i];
      o = s < 0;
      if (o) s += base;
      ret.a[i] = s;
    }
    if (ret.len() > 1 && !ret.a.back()) ret.a.pop_back();
    return ret;
  }
  inline friend lnum operator*(const lnum &l, const lnum &r) {
    lnum ret(0, l.base);
    int base = l.base;
    if (l.len() * r.len() > 1000000) {
      vector<complex<long double> > fa(l.a.begin(), l.a.end()),
          fb(r.a.begin(), r.a.end());
      int n = 1;
      while (n < max(l.len(), r.len())) n <<= 1;
      n <<= 1;
      fa.resize(n), fb.resize(n);
      fft(fa, false), fft(fb, false);
      for (int i = 0; i < n; ++i) fa[i] *= fb[i];
      fft(fa, true);
      ret.a.resize(n);
      for (int i = 0; i < n; ++i) ret.a[i] = int(fa[i].real() + 0.5);
      int carry = 0;
      for (int i = 0; i < n; ++i) {
        ret.a[i] += carry;
        carry = ret.a[i] / base;
        ret.a[i] %= base;
      }
    } else {
      ret.a.resize(l.len() + r.len());
      for (int i = 0; i < l.len(); ++i)
        for (int j = 0, carry = 0; j < r.len() || carry; ++j) {
          long long cur = ret.a[i + j] +
                          (long long)l.a[i] * (j < r.len() ? r.a[j] : 0) +
                          carry;
          ret.a[i + j] = cur % base;
          carry = cur / base;
        }
    }
    while (ret.len() > 1 && !ret.a.back()) ret.a.pop_back();
    return ret;
  }
  inline friend lnum operator/(const lnum &l, const int &r) {
    lnum ret(0, l.base);
    ret.a.resize(l.len());
    int carry = 0;
    for (int i = l.len() - 1; i >= 0; --i) {
      long long cur = l.a[i] + (long long)carry * l.base;
      ret.a[i] = cur / r;
      carry = cur % r;
    }
    while (ret.len() > 1 && ret.a.back() == 0) ret.a.pop_back();
    return ret;
  }
  inline friend bool operator<(const lnum &l, const lnum &r) {
    if (l.len() < r.len()) return true;
    if (l.len() > r.len()) return false;
    int n = l.len();
    for (int i = n - 1; i >= 0; --i) {
      if (l.a[i] < r.a[i]) return true;
      if (l.a[i] > r.a[i]) return false;
    }
    return false;
  }
  inline friend bool operator>(const lnum &l, const lnum &r) { return r < l; }
  inline friend bool operator==(const lnum &l, const lnum &r) {
    if (l.len() != r.len()) return false;
    int n = l.len();
    for (int i = n - 1; i; --i) {
      if (l.a[i] != r.a[i]) return false;
    }
    return true;
  }
  inline friend bool operator!=(const lnum &l, const lnum &r) {
    return !(l == r);
  }
  inline void print() {
    if (base == 1000000000) {
      printf("%d", a.back());
      for (int i = a.size() - 2; i >= 0; --i) printf("%09d", a[i]);
    } else {
      for (int i = a.size() - 1; i >= 0; --i) printf("%d", a[i]);
    }
  }
};
int main() {
  int(n);
  input((n));
  ;
  if (n == 1) {
    int a = nxt();
    if (a)
      puts("BitLGM");
    else
      puts("BitAryo");
    return 0;
  }
  if (n == 2) {
    int a = nxt();
    int b = nxt();
    char dp[a + 1][b + 1];
    memset((dp), 0, sizeof(dp));
    for (int i = 0; i < (int)(a + 1); i++)
      for (int j = 0; j < (int)(b + 1); j++) {
        for (int k = (1); k <= (int)(i); k++)
          if (!dp[i - k][j]) {
            dp[i][j] = 1;
            break;
          }
        for (int k = (1); k <= (int)(j); k++)
          if (!dp[i][j - k]) {
            dp[i][j] = 1;
            break;
          }
        for (int k = (1); k <= (int)(min(i, j)); k++)
          if (!dp[i - k][j - k]) {
            dp[i][j] = 1;
            break;
          }
      }
    puts(dp[a][b] ? "BitLGM" : "BitAryo");
    return 0;
  }
  int a = nxt();
  int b = nxt();
  int c = nxt();
  char dp[a + 1][b + 1][c + 1];
  memset((dp), 0, sizeof(dp));
  int cnt = 0;
  for (int i = 0; i <= a; ++i) {
    for (int j = 0; j <= b; ++j) {
      for (int k = 0; k <= c; ++k) {
        if (!dp[i][j][k]) {
          for (int q = (i + 1); q <= (int)(a); q++) dp[q][j][k] = 1;
          for (int q = (j + 1); q <= (int)(b); q++) dp[i][q][k] = 1;
          for (int q = (k + 1); q <= (int)(c); q++) dp[i][j][q] = 1;
          for (int q = (1); q <= (int)(min(a - i, min(b - j, c - k))); q++)
            dp[i + q][j + q][k + q] = 1;
        }
      }
    }
  }
  puts(dp[a][b][c] ? "BitLGM" : "BitAryo");
  return 0;
}

### Prompt

Create a solution in cpp for the following problem:

Since most contestants do not read this part, I have to repeat that Bitlandians are quite weird. They have their own jobs, their own working method, their own lives, their own sausages and their own games!

Since you are so curious about Bitland, I'll give you the chance of peeking at one of these games.

BitLGM and BitAryo are playing yet another of their crazy-looking genius-needed Bitlandish games. They've got a sequence of n non-negative integers a1, a2, ..., an. The players make moves in turns. BitLGM moves first. Each player can and must do one of the two following actions in his turn:

  * Take one of the integers (we'll denote it as ai). Choose integer x (1 ≤ x ≤ ai). And then decrease ai by x, that is, apply assignment: ai = ai - x. 
  * Choose integer x <image>. And then decrease all ai by x, that is, apply assignment: ai = ai - x, for all i. 



The player who cannot make a move loses.

You're given the initial sequence a1, a2, ..., an. Determine who wins, if both players plays optimally well and if BitLGM and BitAryo start playing the described game in this sequence.

Input

The first line contains an integer n (1 ≤ n ≤ 3).

The next line contains n integers a1, a2, ..., an (0 ≤ ai < 300).

Output

Write the name of the winner (provided that both players play optimally well). Either "BitLGM" or "BitAryo" (without the quotes).

Examples

Input

2
1 1


Output

BitLGM


Input

2
1 2


Output

BitAryo


Input

3
1 2 1


Output

BitLGM

### Response

```cpp
#include <bits/stdc++.h>
int clock0 = clock();
using namespace std;
template <class _T>
inline _T sqr(const _T &first) {
  return first * first;
}
template <class _T>
inline string tostr(const _T &a) {
  ostringstream os("");
  os << a;
  return os.str();
}
const long double PI = 3.1415926535897932384626433832795L;
const long double EPS = 1e-9;
char TEMPORARY_CHAR;
const int INF = 2e9;
inline void fft(vector<complex<long double> > &a, bool invert) {
  int n = (int)a.size();
  for (int i = 1, j = 0; i < n; ++i) {
    int bit = n >> 1;
    for (; j >= bit; bit >>= 1) j -= bit;
    j += bit;
    if (i < j) swap(a[i], a[j]);
  }
  for (int len = 2; len <= n; len <<= 1) {
    long double ang = 2 * PI / len * (invert ? -1 : 1);
    complex<long double> wlen(cos(ang), sin(ang));
    for (int i = 0; i < n; i += len) {
      complex<long double> w(1);
      for (int j = 0; j < len / 2; ++j) {
        complex<long double> u = a[i + j], v = a[i + j + len / 2] * w;
        a[i + j] = u + v;
        a[i + j + len / 2] = u - v;
        w *= wlen;
      }
    }
  }
  if (invert)
    for (int i = 0; i < n; ++i) a[i] /= n;
}
inline void input(int &a) {
  a = 0;
  while (((TEMPORARY_CHAR = getchar()) > '9' || TEMPORARY_CHAR < '0') &&
         (TEMPORARY_CHAR != '-')) {
  }
  char neg = 0;
  if (TEMPORARY_CHAR == '-') {
    neg = 1;
    TEMPORARY_CHAR = getchar();
  }
  while (TEMPORARY_CHAR <= '9' && TEMPORARY_CHAR >= '0') {
    a = (a << 3) + (a << 1) + TEMPORARY_CHAR - '0';
    TEMPORARY_CHAR = getchar();
  }
  if (neg) a = -a;
}
inline void out(int a) {
  if (!a) putchar('0');
  if (a < 0) {
    putchar('-');
    a = -a;
  }
  char s[10];
  int i;
  for (i = 0; a; ++i) {
    s[i] = '0' + a % 10;
    a /= 10;
  }
  for (int j = (i)-1; j >= 0; j--) putchar(s[j]);
}
inline int nxt() {
  int(ret);
  input((ret));
  ;
  return ret;
}
struct lnum {
  vector<int> a;
  int base;
  lnum(int num = 0, int base = 1000000000) : base(base) {
    if (!num) a.resize(1);
    while (num) {
      a.push_back(num % base);
      num /= base;
    }
  }
  inline int len() const { return a.size(); }
  lnum &operator=(const lnum &l) {
    if (this != &l) {
      a = l.a;
      base = l.base;
    }
    return *this;
  }
  inline friend lnum operator+(const lnum &l, const lnum &r) {
    lnum ret(0, l.base);
    int base = l.base;
    int ln = l.len(), rn = r.len();
    int n = max(ln, rn);
    ret.a.resize(n);
    int o = 0;
    for (int i = 0; i < n; ++i) {
      int s = o;
      if (i < ln) s += l.a[i];
      if (i < rn) s += r.a[i];
      o = s >= base;
      if (o) s -= base;
      ret.a[i] = s;
    }
    if (o) ret.a.push_back(1);
    return ret;
  }
  inline friend lnum operator-(const lnum &l, const lnum &r) {
    lnum ret(0, l.base);
    int base = l.base;
    int n = l.len();
    int rn = r.len();
    ret.a.resize(n);
    int o = 0;
    for (int i = 0; i < n; ++i) {
      int s = l.a[i] - o;
      if (i < rn) s -= r.a[i];
      o = s < 0;
      if (o) s += base;
      ret.a[i] = s;
    }
    if (ret.len() > 1 && !ret.a.back()) ret.a.pop_back();
    return ret;
  }
  inline friend lnum operator*(const lnum &l, const lnum &r) {
    lnum ret(0, l.base);
    int base = l.base;
    if (l.len() * r.len() > 1000000) {
      vector<complex<long double> > fa(l.a.begin(), l.a.end()),
          fb(r.a.begin(), r.a.end());
      int n = 1;
      while (n < max(l.len(), r.len())) n <<= 1;
      n <<= 1;
      fa.resize(n), fb.resize(n);
      fft(fa, false), fft(fb, false);
      for (int i = 0; i < n; ++i) fa[i] *= fb[i];
      fft(fa, true);
      ret.a.resize(n);
      for (int i = 0; i < n; ++i) ret.a[i] = int(fa[i].real() + 0.5);
      int carry = 0;
      for (int i = 0; i < n; ++i) {
        ret.a[i] += carry;
        carry = ret.a[i] / base;
        ret.a[i] %= base;
      }
    } else {
      ret.a.resize(l.len() + r.len());
      for (int i = 0; i < l.len(); ++i)
        for (int j = 0, carry = 0; j < r.len() || carry; ++j) {
          long long cur = ret.a[i + j] +
                          (long long)l.a[i] * (j < r.len() ? r.a[j] : 0) +
                          carry;
          ret.a[i + j] = cur % base;
          carry = cur / base;
        }
    }
    while (ret.len() > 1 && !ret.a.back()) ret.a.pop_back();
    return ret;
  }
  inline friend lnum operator/(const lnum &l, const int &r) {
    lnum ret(0, l.base);
    ret.a.resize(l.len());
    int carry = 0;
    for (int i = l.len() - 1; i >= 0; --i) {
      long long cur = l.a[i] + (long long)carry * l.base;
      ret.a[i] = cur / r;
      carry = cur % r;
    }
    while (ret.len() > 1 && ret.a.back() == 0) ret.a.pop_back();
    return ret;
  }
  inline friend bool operator<(const lnum &l, const lnum &r) {
    if (l.len() < r.len()) return true;
    if (l.len() > r.len()) return false;
    int n = l.len();
    for (int i = n - 1; i >= 0; --i) {
      if (l.a[i] < r.a[i]) return true;
      if (l.a[i] > r.a[i]) return false;
    }
    return false;
  }
  inline friend bool operator>(const lnum &l, const lnum &r) { return r < l; }
  inline friend bool operator==(const lnum &l, const lnum &r) {
    if (l.len() != r.len()) return false;
    int n = l.len();
    for (int i = n - 1; i; --i) {
      if (l.a[i] != r.a[i]) return false;
    }
    return true;
  }
  inline friend bool operator!=(const lnum &l, const lnum &r) {
    return !(l == r);
  }
  inline void print() {
    if (base == 1000000000) {
      printf("%d", a.back());
      for (int i = a.size() - 2; i >= 0; --i) printf("%09d", a[i]);
    } else {
      for (int i = a.size() - 1; i >= 0; --i) printf("%d", a[i]);
    }
  }
};
int main() {
  int(n);
  input((n));
  ;
  if (n == 1) {
    int a = nxt();
    if (a)
      puts("BitLGM");
    else
      puts("BitAryo");
    return 0;
  }
  if (n == 2) {
    int a = nxt();
    int b = nxt();
    char dp[a + 1][b + 1];
    memset((dp), 0, sizeof(dp));
    for (int i = 0; i < (int)(a + 1); i++)
      for (int j = 0; j < (int)(b + 1); j++) {
        for (int k = (1); k <= (int)(i); k++)
          if (!dp[i - k][j]) {
            dp[i][j] = 1;
            break;
          }
        for (int k = (1); k <= (int)(j); k++)
          if (!dp[i][j - k]) {
            dp[i][j] = 1;
            break;
          }
        for (int k = (1); k <= (int)(min(i, j)); k++)
          if (!dp[i - k][j - k]) {
            dp[i][j] = 1;
            break;
          }
      }
    puts(dp[a][b] ? "BitLGM" : "BitAryo");
    return 0;
  }
  int a = nxt();
  int b = nxt();
  int c = nxt();
  char dp[a + 1][b + 1][c + 1];
  memset((dp), 0, sizeof(dp));
  int cnt = 0;
  for (int i = 0; i <= a; ++i) {
    for (int j = 0; j <= b; ++j) {
      for (int k = 0; k <= c; ++k) {
        if (!dp[i][j][k]) {
          for (int q = (i + 1); q <= (int)(a); q++) dp[q][j][k] = 1;
          for (int q = (j + 1); q <= (int)(b); q++) dp[i][q][k] = 1;
          for (int q = (k + 1); q <= (int)(c); q++) dp[i][j][q] = 1;
          for (int q = (1); q <= (int)(min(a - i, min(b - j, c - k))); q++)
            dp[i + q][j + q][k + q] = 1;
        }
      }
    }
  }
  puts(dp[a][b][c] ? "BitLGM" : "BitAryo");
  return 0;
}

```