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;
mt19937 mr(time(0));
struct LL {
  static long long int m;
  long long int val;
  LL(long long int v) { val = reduce(v); };
  LL(int v) { val = reduce((long long int)v); };
  LL() { val = 0; };
  ~LL(){};
  LL(const LL& l) { val = l.val; };
  LL& operator=(int l) {
    val = l;
    return *this;
  }
  LL& operator=(long long int l) {
    val = l;
    return *this;
  }
  LL& operator=(LL l) {
    val = l.val;
    return *this;
  }
  static void setMod(long long int m) {
    assert(m);
    LL::m = m;
  }
  static long long int reduce(long long int x, long long int md = m) {
    x %= md;
    while (x >= md) x -= md;
    while (x < 0) x += md;
    return x;
  }
  bool operator<(const LL& b) { return val < b.val; }
  bool operator<=(const LL& b) { return val <= b.val; }
  bool operator!=(const LL& b) { return val != b.val; }
  bool operator==(const LL& b) { return val == b.val; }
  bool operator>=(const LL& b) { return val >= b.val; }
  bool operator>(const LL& b) { return val > b.val; }
  LL operator+(const LL& b) { return LL(val + b.val); }
  LL operator+(const long long int& b) { return (*this + LL(b)); }
  LL& operator+=(const LL& b) { return (*this = *this + b); }
  LL& operator+=(const long long int& b) { return (*this = *this + b); }
  LL operator-(const LL& b) { return LL(val - b.val); }
  LL operator-(const long long int& b) { return (*this - LL(b)); }
  LL& operator-=(const LL& b) { return (*this = *this - b); }
  LL& operator-=(const long long int& b) { return (*this = *this - b); }
  LL operator*(const LL& b) { return LL(val * b.val); }
  LL operator*(const long long int& b) { return (*this * LL(b)); }
  LL& operator*=(const LL& b) { return (*this = *this * b); }
  LL& operator*=(const long long int& b) { return (*this = *this * b); }
  static LL exp(const LL& x, const long long int& y) {
    long long int z = y;
    z = reduce(z, m - 1);
    LL ret = 1;
    LL w = x;
    while (z) {
      if (z & 1) ret *= w;
      z >>= 1;
      w *= w;
    }
    return ret;
  }
  LL& operator^=(long long int y) { return (*this = LL(val ^ y)); }
  LL operator/(const LL& b) { return ((*this) * exp(b, -1)); }
  LL operator/(const long long int& b) { return (*this / LL(b)); }
  LL operator/=(const LL& b) { return ((*this) *= exp(b, -1)); }
  LL& operator/=(const long long int& b) { return (*this = *this / LL(b)); }
};
ostream& operator<<(ostream& os, const LL& obj) { return os << obj.val; }
long long int LL::m = 1000000007;
using namespace std;
long long int cases, N, M, Q, K, X, Y;
long long int rd() {
  long long int x;
  cin >> x;
  return x;
}
double rdd() {
  double x;
  cin >> x;
  return x;
}
string rds() {
  string x;
  cin >> x;
  return x;
}
template <class T>
void rds(char* S, T* sz) {
  *sz = strlen(strcpy(S, rds().c_str()));
}
template <class T>
void rG(int sz, vector<vector<T>>& adj, int E = -18852946) {
  if (E == -18852946) E = sz - 1;
  adj.clear();
  for (long long int i = 0; i < sz + 1; ++i) adj.push_back(vector<T>());
  for (long long int i = 0; i < E; ++i) {
    T a = rd();
    T b = rd();
    adj[a].push_back(b);
    adj[b].push_back(a);
  }
}
void fl() { cout.flush(); }
template <class T>
void ds(vector<T> v) {
  for (auto x : v) cout << x << " ";
  cout << endl;
}
template <class T>
void panic(T out) {
  cout << out << endl;
  exit(0);
}
template <class S, class T>
bool updmin(S& a, T b) {
  S B = (S)b;
  if (B < a) {
    a = B;
    return 1;
  }
  return 0;
}
template <class S, class T>
bool updmax(S& a, T b) {
  S B = (S)b;
  if (B > a) {
    a = B;
    return 1;
  }
  return 0;
}
template <class S, class T>
S min(S a, T b) {
  S c = a;
  updmin(c, b);
  return c;
}
template <class S, class T>
S max(S a, T b) {
  S c = a;
  updmax(c, b);
  return c;
}
long long int gcd(long long int a, long long int b) {
  return b ? gcd(b, a % b) : a;
}
void precalc() {}
void reset() {}
bool cmp(pair<int, int> a, pair<int, int> b) {}
int L, A, B, R;
int S[3 * 100010];
void read() {
  N = rd();
  for (long long int i = 1; i <= N; ++i) S[i] = rd();
  S[0] = S[N + 1] = -99999;
  L = 1;
  R = N;
  for (A = 1; S[A + 1] > S[A]; A++) {
  }
  for (B = N; S[B - 1] > S[B]; B--) {
  }
  cout << ((((A - 1) & 1) && ((N - B) & 1)) ? "Bob" : "Alice") << endl;
}
int main() {
  precalc();
  bool trials = 0;
  bool interactive = 0;
  if (!interactive) {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
  }
  if (trials)
    cases = rd();
  else
    cases = 1;
  while (cases--) {
    read();
  }
}
