#include <bits/stdc++.h>
using namespace std;
string to_string(char x) { return (string) "\'" + x + "\'"; }
string to_string(const string &x) { return '\"' + x + '\"'; }
string to_string(const char *x) { return to_string((string)x); }
string to_string(bool x) { return x ? "true" : "false"; }
template <typename T, typename V>
string to_string(const pair<T, V> &x) {
  return '(' + to_string(x.first) + ',' + to_string(x.second) + ')';
}
template <typename T>
string to_string(const T &x) {
  int f = 0;
  string r;
  for (auto &i : x) r += (f++ ? "," : "") + to_string(i);
  return '{' + r + '}';
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  cerr << to_string(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
const int MAXN = 3e5 + 5;
const long long mod = (long long)1e9 + 7;
const long long N = 5;
const long long M = 4;
void solution() {
  long long n;
  cin >> n;
  vector<long long> A(n + 1);
  A[0] = -INT_MAX;
  for (long long i = 1; i <= n; i++) cin >> A[i];
  long long left = 1;
  while (left <= n && A[left] < A[left + 1]) left++;
  long long right = n;
  while (right > 0 && A[right] < A[right - 1]) right--;
  long long cnt1 = left, cnt2 = n - right + 1;
  if ((cnt1 % 2 == 0) && (cnt2 % 2 == 0)) {
    cout << "Bob" << '\n';
  } else {
    cout << "Alice" << '\n';
  }
}
int32_t main() {
  cin.tie(nullptr);
  cout.tie(0);
  ios_base::sync_with_stdio(false);
  long long testcase = 1;
  while (testcase--) solution();
  return 0;
}

### Prompt

Create a solution in cpp for the following problem:

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>
using namespace std;
string to_string(char x) { return (string) "\'" + x + "\'"; }
string to_string(const string &x) { return '\"' + x + '\"'; }
string to_string(const char *x) { return to_string((string)x); }
string to_string(bool x) { return x ? "true" : "false"; }
template <typename T, typename V>
string to_string(const pair<T, V> &x) {
  return '(' + to_string(x.first) + ',' + to_string(x.second) + ')';
}
template <typename T>
string to_string(const T &x) {
  int f = 0;
  string r;
  for (auto &i : x) r += (f++ ? "," : "") + to_string(i);
  return '{' + r + '}';
}
void _print() { cerr << "]\n"; }
template <typename T, typename... V>
void _print(T t, V... v) {
  cerr << to_string(t);
  if (sizeof...(v)) cerr << ", ";
  _print(v...);
}
const int MAXN = 3e5 + 5;
const long long mod = (long long)1e9 + 7;
const long long N = 5;
const long long M = 4;
void solution() {
  long long n;
  cin >> n;
  vector<long long> A(n + 1);
  A[0] = -INT_MAX;
  for (long long i = 1; i <= n; i++) cin >> A[i];
  long long left = 1;
  while (left <= n && A[left] < A[left + 1]) left++;
  long long right = n;
  while (right > 0 && A[right] < A[right - 1]) right--;
  long long cnt1 = left, cnt2 = n - right + 1;
  if ((cnt1 % 2 == 0) && (cnt2 % 2 == 0)) {
    cout << "Bob" << '\n';
  } else {
    cout << "Alice" << '\n';
  }
}
int32_t main() {
  cin.tie(nullptr);
  cout.tie(0);
  ios_base::sync_with_stdio(false);
  long long testcase = 1;
  while (testcase--) solution();
  return 0;
}

```