description: 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
solution: #include <bits/stdc++.h>
  using namespace std;
  const long long mod = 1e9 + 7;
  long long cl(long double a) {
    if (a > (long long)a) {
      return (long long)a + 1;
    } else {
      return (long long)a;
    }
  }
  long long flr(long double a) {
    if (a < 0.0) {
      return (long long)a - 1;
    }
    return (long long)a;
  }
  long long gcd(long long a, long long b) {
    if (b == 0)
      return a;
    else
      return gcd(b, a % b);
  }
  long long pw(long long n, long long k) {
    if (k == 0) return 1;
    long long t = pw(n, k / 2);
    long long ans = (t * t) % mod;
    if (k % 2)
      return (ans * n) % mod;
    else
      return ans;
  }
  long long solve() {
    long long n;
    cin >> n;
    long long a[n];
    for (long long i = 0; i < n; i++) cin >> a[i];
    long long pre[n], suff[n];
    for (long long i = 0; i < n; i++) {
      pre[i] = 1;
      if (i > 0 && a[i] < a[i - 1]) {
        pre[i] = pre[i - 1] + 1;
      }
    }
    for (long long i = n - 1; i >= 0; i--) {
      suff[i] = 1;
      if (i < n - 1 && a[i] < a[i + 1]) {
        suff[i] += suff[i + 1];
      }
    }
    long long s = 0, e = n - 1;
    long long flag = 0;
    long long prev = -1;
    while (s <= e) {
      if (a[s] > prev && a[e] > prev) {
        if (a[e] < a[s]) {
          long long len = min(e - s + 1, suff[s]);
          if (len % 2) {
            return flag;
          }
          prev = a[e];
          e--;
        } else if (a[e] > a[s]) {
          long long len = min(e - s + 1, pre[e]);
          if (len % 2) {
            return flag;
          }
          prev = a[s];
          s++;
        } else {
          long long len = min(e - s + 1, suff[s]);
          if (len % 2) return flag;
          len = min(e - s + 1, pre[e]);
          if (len % 2) return flag;
          return (flag ^ 1);
        }
      } else if (a[e] > prev) {
        long long len = min(e - s + 1, pre[e]);
        if (len % 2)
          return flag;
        else
          return (flag ^ 1);
      } else if (a[s] > prev) {
        long long len = min(e - s + 1, suff[s]);
        if (len % 2)
          return flag;
        else
          return (flag ^ 1);
      } else {
        return (flag ^ 1);
      }
      flag ^= 1;
    }
    return flag;
  }
  int32_t main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    long long t;
    t = 1;
    while (t--) {
      if (!solve()) {
        cout << "Alice"
             << "\n";
      } else {
        cout << "Bob"
             << "\n";
      }
    }
  }
  