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: 
  import java.io.*;
  import java.util.*;
  
  public final class Main {
  
      static PrintWriter out = new PrintWriter(System.out);
      static FastReader in = new FastReader();
      static Pair[] moves = new Pair[]{new Pair(-1, 0), new Pair(0, 1), new Pair(1, 0), new Pair(0, -1)};
      static int mod = (int) (1e9 + 7);
      static int mod2 = 998244353;
  
      public static void main(String[] args) {
          int tt = 1;
          while (tt-- > 0) {
              solve();
          }
          out.flush();
      }
  
      public static void solve() {
          int n = i();
          int[] a = input(n);
  
          int left = 0;
          for (int i = 1; i < n; i++) {
              if (a[i] > a[i - 1]) {
                  left++;
              } else {
                  break;
              }
          }
          int right = n - 1;
          for (int i = n - 2; i >= 0; i--) {
              if (a[i] > a[i + 1]) {
                  right--;
              } else {
                  break;
              }
          }
          if (solve(-1, 0, n - 1, left, right, a)) {
              out.println("Alice");
          } else {
              out.println("Bob");
          }
      }
  
      private static boolean solve(int prev, int l, int r, int ll, int rr, int[] a) {
          if (l > r) {
              return false;
          }
          if (a[l] <= prev && a[r] <= prev) {
              return false;
          } else if (a[l] > prev && a[r] > prev) {
              boolean b1 = solve(a[l], l + 1, r, ll, rr, a);
              boolean b2 = solve(a[r], l, r - 1, ll, rr, a);
              return !b1 || !b2;
          } else if (a[l] > prev) {
              return (ll - l) % 2 == 0;
          } else {
              return (r - rr) % 2 == 0;
          }
      }
  
      private static int dfs(int i, int j, boolean[][] vis, int[][] mat) {
          if (vis[i][j]) {
              return 0;
          }
          vis[i][j] = true;
  
          int cur = mat[i][j];
          int d = 1;
          for (int k = 0; k < 4; k++) {
              if ((cur & (1 << k)) == 0) {
                  int nx = i + moves[3 - k].i;
                  int ny = j + moves[3 - k].j;
                  d += dfs(nx, ny, vis, mat);
              }
          }
          return d;
      }
  
  
      static long[] pre(int[] a) {
          long[] pre = new long[a.length + 1];
          pre[0] = 0;
          for (int i = 0; i < a.length; i++) {
              pre[i + 1] = pre[i] + a[i];
          }
          return pre;
      }
  
      static void print(char A[]) {
          for (char c : A) {
              out.print(c);
          }
          out.println();
      }
  
      static void print(boolean A[]) {
          for (boolean c : A) {
              out.print(c + " ");
          }
          out.println();
      }
  
      static void print(int A[]) {
          for (int c : A) {
              out.print(c + " ");
          }
          out.println();
      }
  
      static void print(long A[]) {
          for (long i : A) {
              out.print(i + " ");
          }
          out.println();
      }
  
      static void print(List<Integer> A) {
          for (int a : A) {
              out.print(a + " ");
          }
      }
  
      static int i() {
          return in.nextInt();
      }
  
      static long l() {
          return in.nextLong();
      }
  
      static String s() {
          return in.nextLine();
      }
  
      static int[][] inputWithIdx(int N) {
          int A[][] = new int[N][2];
          for (int i = 0; i < N; i++) {
              A[i] = new int[]{i, in.nextInt()};
          }
          return A;
      }
  
      static int[] input(int N) {
          int A[] = new int[N];
          for (int i = 0; i < N; i++) {
              A[i] = in.nextInt();
          }
          return A;
      }
  
      static long[] inputLong(int N) {
          long A[] = new long[N];
          for (int i = 0; i < A.length; i++) {
              A[i] = in.nextLong();
          }
          return A;
      }
  
      static int GCD(int a, int b) {
          if (b == 0) {
              return a;
          } else {
              return GCD(b, a % b);
          }
      }
  
      static long GCD(long a, long b) {
          if (b == 0) {
              return a;
          } else {
              return GCD(b, a % b);
          }
      }
  
      static long LCM(int a, int b) {
          return (long) a / GCD(a, b) * b;
      }
  
      static long LCM(long a, long b) {
          return a / GCD(a, b) * b;
      }
  
      static void shuffleAndSort(int[] arr) {
          for (int i = 0; i < arr.length; i++) {
              int rand = (int) (Math.random() * arr.length);
              int temp = arr[rand];
              arr[rand] = arr[i];
              arr[i] = temp;
          }
          Arrays.sort(arr);
      }
  
      static void shuffleAndSort(int[][] arr, Comparator<? super int[]> comparator) {
          for (int i = 0; i < arr.length; i++) {
              int rand = (int) (Math.random() * arr.length);
              int[] temp = arr[rand];
              arr[rand] = arr[i];
              arr[i] = temp;
          }
          Arrays.sort(arr, comparator);
      }
  
      static void shuffleAndSort(long[] arr) {
          for (int i = 0; i < arr.length; i++) {
              int rand = (int) (Math.random() * arr.length);
              long temp = arr[rand];
              arr[rand] = arr[i];
              arr[i] = temp;
          }
          Arrays.sort(arr);
      }
  
      static boolean isPerfectSquare(double number) {
          double sqrt = Math.sqrt(number);
          return ((sqrt - Math.floor(sqrt)) == 0);
      }
  
      static void swap(int A[], int a, int b) {
          int t = A[a];
          A[a] = A[b];
          A[b] = t;
      }
  
      static long pow(long a, long b, int mod) {
          long pow = 1;
          long x = a;
          while (b != 0) {
              if ((b & 1) != 0) {
                  pow = (pow * x) % mod;
              }
              x = (x * x) % mod;
              b /= 2;
          }
          return pow;
      }
  
      static long pow(long a, long b) {
          long pow = 1;
          long x = a;
          while (b != 0) {
              if ((b & 1) != 0) {
                  pow *= x;
              }
              x = x * x;
              b /= 2;
          }
          return pow;
      }
  
      static long modInverse(long x, int mod) {
          return pow(x, mod - 2, mod);
      }
  
      static boolean isPrime(long N) {
          if (N <= 1) {
              return false;
          }
          if (N <= 3) {
              return true;
          }
          if (N % 2 == 0 || N % 3 == 0) {
              return false;
          }
          for (int i = 5; i * i <= N; i = i + 6) {
              if (N % i == 0 || N % (i + 2) == 0) {
                  return false;
              }
          }
          return true;
      }
  
      public static String reverse(String str) {
          if (str == null) {
              return null;
          }
          return new StringBuilder(str).reverse().toString();
      }
  
      public static String repeat(char ch, int repeat) {
          if (repeat <= 0) {
              return "";
          }
          final char[] buf = new char[repeat];
          for (int i = repeat - 1; i >= 0; i--) {
              buf[i] = ch;
          }
          return new String(buf);
      }
  
      public static int[] manacher(String s) {
          char[] chars = s.toCharArray();
          int n = s.length();
          int[] d1 = new int[n];
          for (int i = 0, l = 0, r = -1; i < n; i++) {
              int k = (i > r) ? 1 : Math.min(d1[l + r - i], r - i + 1);
              while (0 <= i - k && i + k < n && chars[i - k] == chars[i + k]) {
                  k++;
              }
              d1[i] = k--;
              if (i + k > r) {
                  l = i - k;
                  r = i + k;
              }
          }
          return d1;
      }
  
      public static int[] kmp(String s) {
          int n = s.length();
          int[] res = new int[n];
          for (int i = 1; i < n; ++i) {
              int j = res[i - 1];
              while (j > 0 && s.charAt(i) != s.charAt(j)) {
                  j = res[j - 1];
              }
              if (s.charAt(i) == s.charAt(j)) {
                  ++j;
              }
              res[i] = j;
          }
          return res;
      }
  }
  
  class Pair {
  
      int i, j;
  
      Pair(int i, int j) {
          this.i = i;
          this.j = j;
      }
  
      @Override
      public boolean equals(Object o) {
          if (this == o) {
              return true;
          }
          if (o == null || getClass() != o.getClass()) {
              return false;
          }
          Pair pair = (Pair) o;
          return i == pair.i && j == pair.j;
      }
  
      @Override
      public int hashCode() {
          return Objects.hash(i, j);
      }
  }
  
  class FastReader {
  
      BufferedReader br;
      StringTokenizer st;
  
      public FastReader() {
          br = new BufferedReader(new InputStreamReader(System.in));
      }
  
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
  
      int nextInt() {
          return Integer.parseInt(next());
      }
  
      long nextLong() {
          return Long.parseLong(next());
      }
  
      double nextDouble() {
          return Double.parseDouble(next());
      }
  
      String nextLine() {
          String str = "";
          try {
              str = br.readLine();
          } catch (IOException e) {
              e.printStackTrace();
          }
          return str;
      }
  }
  
  class Node {
  
      int data, open, close;
  
      Node() {
          this(0, 0, 0);
      }
  
      Node(int data, int open, int close) {
          this.data = data;
          this.open = open;
          this.close = close;
      }
  }
  
  class ST {
  
      int n;
      Node[] st;
  
      ST(int n) {
          this.n = n;
          st = new Node[4 * Integer.highestOneBit(n)];
      }
  
      void build(Node[] nodes) {
          build(0, 0, n - 1, nodes);
      }
  
      private void build(int id, int l, int r, Node[] nodes) {
          if (l == r) {
              st[id] = nodes[l];
              return;
          }
          int mid = (l + r) >> 1;
          build((id << 1) + 1, l, mid, nodes);
          build((id << 1) + 2, mid + 1, r, nodes);
          st[id] = comb(st[(id << 1) + 1], st[(id << 1) + 2]);
      }
  
      void update(int i, Node node) {
          update(0, 0, n - 1, i, node);
      }
  
      private void update(int id, int l, int r, int i, Node node) {
          if (i < l || r < i) {
              return;
          }
          if (l == r) {
              st[id] = node;
              return;
          }
          int mid = (l + r) >> 1;
          update((id << 1) + 1, l, mid, i, node);
          update((id << 1) + 2, mid + 1, r, i, node);
          st[id] = comb(st[(id << 1) + 1], st[(id << 1) + 2]);
      }
  
      Node get(int x, int y) {
          return get(0, 0, n - 1, x, y);
      }
  
      private Node get(int id, int l, int r, int x, int y) {
          if (x > r || y < l) {
              return new Node();
          }
          if (x <= l && r <= y) {
              return st[id];
          }
          int mid = (l + r) >> 1;
          return comb(get((id << 1) + 1, l, mid, x, y), get((id << 1) + 2, mid + 1, r, x, y));
      }
  
      Node comb(Node a, Node b) {
          if (a == null) {
              return b;
          }
          if (b == null) {
              return a;
          }
          int min = Math.min(a.open, b.close);
          return new Node(a.data + b.data + min * 2, a.open + b.open - min, a.close + b.close - min);
      }
  }