Alice and Bob are playing a game. They are given an array A of length N. The array consists of integers. They are building a sequence together. In the beginning, the sequence is empty. In one turn a player can remove a number from the left or right side of the array and append it to the sequence. The rule is that the sequence they are building must be strictly increasing. The winner is the player that makes the last move. Alice is playing first. Given the starting array, under the assumption that they both play optimally, who wins the game?

Input

The first line contains one integer N (1 ≤ N ≤ 2*10^5) - the length of the array A.

The second line contains N integers A_1, A_2,...,A_N (0 ≤ A_i ≤ 10^9)

Output

The first and only line of output consists of one string, the name of the winner. If Alice won, print "Alice", otherwise, print "Bob".

Examples

Input


1
5


Output


Alice


Input


3
5 4 5


Output


Alice


Input


6
5 8 2 1 10 9


Output


Bob
3
5 6 5
 2
5 12

Bob
 Alice

#include <bits/stdc++.h>
using namespace std;
template <typename type_first, typename type_second>
ostream& operator<<(ostream& out, const pair<type_first, type_second> P) {
  out << '{' << P.first << ',' << P.second << '}';
  return out;
}
template <typename type_iterator>
string ite2string(type_iterator begin, type_iterator end) {
  stringstream out;
  bool inserted = false;
  out << '[';
  while (begin != end) {
    out << *begin << ", ";
    inserted = true;
    begin++;
  }
  string ans = out.str();
  if (inserted) {
    ans.pop_back();
    ans.pop_back();
  }
  return ans + ']';
}
template <class stream, class iterable,
          class begin = decltype(begin(declval<iterable>()))>
stream& operator<<(stream& out, const iterable I) {
  out << ite2string(I.begin(), I.end());
  return out;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  unsigned int n;
  cin >> n;
  vector<unsigned int> a(n);
  for (auto& i : a) cin >> i;
  unsigned int l_inc = 1, r_inc = 1;
  for (; l_inc < n and a[l_inc] > a[l_inc - 1]; l_inc++)
    ;
  for (; r_inc < n and a[n - r_inc] < a[n - r_inc - 1]; r_inc++)
    ;
  ;
  ;
  if (l_inc == n and r_inc == n) {
    if (n % 2 == 0) {
      cout << "Bob" << '\n';
    } else {
      cout << "Alice" << '\n';
    }
    exit(0);
  }
  unsigned int li = 0, ri = n - 1;
  unsigned int alice = true;
  int last = -1;
  while (true) {
    ;
    if (l_inc == 0 or last >= int(a[ri])) {
      if (r_inc % 2 == 1) {
        if (alice) {
          cout << "Alice" << '\n';
        } else {
          cout << "Bob" << '\n';
        }
      } else {
        if (alice) {
          cout << "Bob" << '\n';
        } else {
          cout << "Alice" << '\n';
        }
      }
      break;
    }
    if (r_inc == 0 or last >= int(a[li])) {
      if (l_inc % 2 == 1) {
        if (alice) {
          cout << "Alice" << '\n';
        } else {
          cout << "Bob" << '\n';
        }
      } else {
        if (alice) {
          cout << "Bob" << '\n';
        } else {
          cout << "Alice" << '\n';
        }
      }
      break;
    }
    if (a[li] > a[ri]) {
      if (l_inc % 2 == 1) {
        if (alice) {
          cout << "Alice" << '\n';
        } else {
          cout << "Bob" << '\n';
        }
        break;
      } else {
        r_inc--;
        ri--;
      }
    } else if (a[ri] > a[li]) {
      if (r_inc % 2 == 1) {
        if (alice) {
          cout << "Alice" << '\n';
        } else {
          cout << "Bob" << '\n';
        }
        break;
      } else {
        l_inc--;
        li++;
      }
    } else {
      if (r_inc % 2 == 1 or l_inc % 2 == 1) {
        if (alice) {
          cout << "Alice" << '\n';
        } else {
          cout << "Bob" << '\n';
        }
        break;
      } else {
        if (alice) {
          cout << "Bob" << '\n';
        } else {
          cout << "Alice" << '\n';
        }
      }
      break;
    }
  }
  return 0;
}
