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.io.IOException;
import java.io.InputStream;
import java.util.InputMismatchException;


public class ArrayGame {


    public static void main(String[] args) {
        Reader s = new Reader();
        int n = s.nextInt();
        int[] a = new int[n];
        int[] left = new int[n];
        int[] right = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = s.nextInt();
        }

        int i = n - 1;
        left[i] = 1;
        i--;
        while (i >= 0) {
            if (a[i] < a[i + 1]) {
                left[i] = 1 + left[i + 1];
            } else {
                left[i] = 1;
            }
            i--;
        }

        i = 0;
        right[i] = 1;
        i++;
        while (i < n) {
            if (a[i] < a[i - 1]) {
                right[i] = 1 + right[i - 1];
            } else {
                right[i] = 1;
            }
            i++;
        }


        System.out.println(call(a, left, right, 0, n - 1, 0, -1) == 0 ? "Alice" : "Bob");
    }

    static int call(int[] a, int[] left, int[] right, int l, int r, int caller, int prev) {
       // System.out.println("Calling with l= " + l + " and right r = " + r + " with caller "+ caller);

        if (l == r || l + 1 == r) {
            return caller;
        }
        if (a[l] > prev && a[r] > prev) {
            if (a[l] >= a[r]) {
                int len = Math.min(r - l, left[l + 1]);
                if (len % 2 == 0) {
                    return caller;
                }
                return call(a, left, right, l, r - 1, (caller + 1) % 2, a[r]);
            } else if (a[r] > a[l]) {
                int len = Math.min(r - l, right[r - 1]);
                if (len % 2 == 0) {
                    return caller;
                }
                return call(a, left, right, l + 1, r, (caller + 1) % 2, a[l]);
            }
        } else if (a[l] > prev) {
            int len = Math.min(r - l, left[l + 1]);
            if (len % 2 == 0) {
                return caller;
            }
            return call(a, left, right, l + 1, r, (caller + 1) % 2, a[l]);
        } else if (a[r] > prev) {
            int len = Math.min(r - l, right[r - 1]);
            if (len % 2 == 0) {
                return caller;
            }
            return call(a, left, right, l, r - 1, (caller + 1) % 2, a[r]);
        }
        return (caller + 1) % 2;
    }


    static class Reader {

        private InputStream mIs;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public Reader() {
            this(System.in);
        }

        public Reader(InputStream is) {
            mIs = is;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();

            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = mIs.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public String next() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

    }

}
