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

from sys import stdin
eg=False
inp=[]
it0=0
it1=0
new=[]


it=0

max1=-1
max2=-1

va=0

for line in stdin:
    if(va==1):
        inp = [x for x in line.strip().split()]
    va+=1

l=len(inp)

def only_one_end(it,lr):
    global inp
    global l
    if(lr):
        n1=int(inp[l-it-1])
        n2=int(inp[l-it-2])
        while(n2>n1):
            it+=1
            n1=n2
            n2=int(inp[l-it-2])
    else:
        n1=int(inp[0+it])
        n2=int(inp[0+it+1])
        while(n2>n1):
            it+=1
            n1=n2
            n2=int(inp[0+it+1])
    it+=1
    return it
            

la=False

for i in range(l):
    n1=int(inp[it0])
    n2=int(inp[l-it1-1])
    if(n1>n2):
        la=True
        new.append(1)
        it1+=1
        if(n2>=int(inp[l-it1-1])):
            it0=only_one_end(it0,False)
            break
    elif (n1<n2):
        la=False
        new.append(0)
        it0+=1
        if(n1>=int(inp[0+it0])):
            it1=only_one_end(it1,True)
            break
    elif(it0!=l-it1-1):
        eg=True
        egPo=[it0,it1]
        it1=only_one_end(it1,True)
        it0=only_one_end(it0,False)
        break
    else:
        if(la):
            it0+=1
        else:
            it1+=1
        break


it3=0
res=False
con=True
for e in new:
    if((e==1 and it0%2==1) or (e==0 and it1%2==1)):
        con=False
        if(res):
            print("Bob")
        else:
            print("Alice")
        break
    elif(e==0):
        it0-=1
    else:
        it1-=1
    res= not res

if(con):
    if((it0+it1)!=0 and (it0%2==0 and it0%2==0)):
        res= not res

    if(res):
        print("Bob")
    else:
        print("Alice")
