#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
using namespace std;
using ll = long long;
using ull = unsigned long long;
template <typename T>
void print(vector<T> v) {
  for (T i : v) cout << i << " ";
  cout << '\n';
}
template <typename T>
void print(vector<vector<T>>& v) {
  for (vector<T>& vv : v) {
    for (T& i : vv) cout << i << " ";
    cout << '\n';
  }
}
template <typename T>
void print(T&& t) {
  cout << t << '\n';
}
template <typename T, typename... Args>
void print(T&& t, Args&&... args) {
  cout << t << " ";
  print(forward<Args>(args)...);
}
template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
  for (auto& i : v) is >> i;
  return is;
}
template <typename T>
ostream& operator<<(ostream& os, vector<T>& v) {
  for (auto& i : v) os << i << ' ';
  return os;
}
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char* x) { cerr << '\"' << x << '\"'; }
void __print(const string& x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V>& x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T& x) {
  int f = 0;
  cerr << '{';
  for (auto& i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
void loop() {
  ll n;
  cin >> n;
  vector<ll> a(n);
  cin >> a;
  if (n == 1) {
    print("Alice");
    return;
  }
  vector<ll> inc, dec;
  inc.push_back(a[0]);
  for (ll i = 0; i < n - 1; i++) {
    if (a[i] < a[i + 1]) {
      inc.push_back(a[i + 1]);
    } else
      break;
  }
  dec.push_back(a[n - 1]);
  for (ll i = n - 1; i > 0; i--) {
    if (a[i] < a[i - 1]) {
      dec.push_back(a[i - 1]);
    } else
      break;
  }
  if (dec.size() % 2) {
    print("Alice");
    return;
  } else if ((inc.size() - 1 + dec.size()) % 2 == 0) {
    print("Alice");
    return;
  }
  print("Bob");
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ll t;
  t = 1;
  while (t--) {
    loop();
  }
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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

### Response

```cpp
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
using namespace std;
using ll = long long;
using ull = unsigned long long;
template <typename T>
void print(vector<T> v) {
  for (T i : v) cout << i << " ";
  cout << '\n';
}
template <typename T>
void print(vector<vector<T>>& v) {
  for (vector<T>& vv : v) {
    for (T& i : vv) cout << i << " ";
    cout << '\n';
  }
}
template <typename T>
void print(T&& t) {
  cout << t << '\n';
}
template <typename T, typename... Args>
void print(T&& t, Args&&... args) {
  cout << t << " ";
  print(forward<Args>(args)...);
}
template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
  for (auto& i : v) is >> i;
  return is;
}
template <typename T>
ostream& operator<<(ostream& os, vector<T>& v) {
  for (auto& i : v) os << i << ' ';
  return os;
}
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char* x) { cerr << '\"' << x << '\"'; }
void __print(const string& x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template <typename T, typename V>
void __print(const pair<T, V>& x) {
  cerr << '{';
  __print(x.first);
  cerr << ',';
  __print(x.second);
  cerr << '}';
}
template <typename T>
void __print(const T& x) {
  int f = 0;
  cerr << '{';
  for (auto& i : x) cerr << (f++ ? "," : ""), __print(i);
  cerr << "}";
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  __print(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
void loop() {
  ll n;
  cin >> n;
  vector<ll> a(n);
  cin >> a;
  if (n == 1) {
    print("Alice");
    return;
  }
  vector<ll> inc, dec;
  inc.push_back(a[0]);
  for (ll i = 0; i < n - 1; i++) {
    if (a[i] < a[i + 1]) {
      inc.push_back(a[i + 1]);
    } else
      break;
  }
  dec.push_back(a[n - 1]);
  for (ll i = n - 1; i > 0; i--) {
    if (a[i] < a[i - 1]) {
      dec.push_back(a[i - 1]);
    } else
      break;
  }
  if (dec.size() % 2) {
    print("Alice");
    return;
  } else if ((inc.size() - 1 + dec.size()) % 2 == 0) {
    print("Alice");
    return;
  }
  print("Bob");
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ll t;
  t = 1;
  while (t--) {
    loop();
  }
}

```