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

import java.util.Arrays;
import java.util.Scanner;

public class ArrayGame {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int a = scanner.nextInt();
        long[] n = new long[a];
        for(int i = 0 ; i < a ; i++) {
            n[i] = scanner.nextLong();
        }
//        System.out.println(a);
//        for(int t : n) {
//            System.out.println(t);
//        }
        int step = 0;
        if(canMove(n, 0)) {
            step = move(n, 0, 0);
        }
//        System.out.println("總移動步數：" + step);
        if(step % 2 == 1)
            System.out.println("Alice");
        else
            System.out.println("Bob");
        System.exit(0);
    }

    public static int move(long[] n, long seq, int step) {
//        for(int i : n) {
//            System.out.print("陣列:" + i + ", ");
//        }
//        System.out.println("Step:" + step);
            // 有路可走
        ++step;
        if(n[0] > n[n.length - 1] && n[0] > seq) {
            // 移動左邊；若左右相等則移動左邊
            seq = n[0];
            n = Arrays.copyOfRange(n, 1, n.length - 1);
//                System.out.println("移動左:" + n[0]);
            if(canMove(n, seq)) {
                return move(n, seq, step);
            }
        }
        else if(n[n.length - 1] > n[0] && n[n.length - 1] > seq) {
            seq = n[n.length - 1];
            n = Arrays.copyOfRange(n, 0, n.length - 1);
            if(canMove(n, seq)) {
                return move(n, seq, step);
            }
        }
        return step;
    }

    public static boolean canMove(long[] n, long seq) {
        boolean b = true;
        if(n == null || n.length < 1) {
            b = false;
        }
        else{
            if(n[0] <= seq && n[n.length - 1] <= seq){
                b = false;
            }
            else {
                b = true;
            }
        }
        return b;
    }
}
