Problem Description

Alice and Bob are playing a game.

They have $n$ piles of stones, with the $i$-th pile containing $a_i$ stones. It is guaranteed that initially $a_i \leq a_{i + 1}$ for $1 \leq i < n$. They take turns performing actions on these piles of stones. In each turn, a player can choose a pile of stones such that $a_i > a_{i - 1}$ (considering $a_0$ as $0$) and remove one stone from it. The player who cannot make a move loses. Alice starts first, and both players use optimal strategies. Determine who will win the game.

Input Format

The first line contains an integer $n(1 \leq n \leq 100)$, representing the number of piles of stones.

The next line contains $n$ numbers, where the $i$-th number is $a_i(1 \leq a_i \leq 10^9)$, as described above.

Output Format

Output "Alice" or "Bob", indicating who will win.

Sample Input and Output

Sample Input #1

1
1

Sample Output #1

Alice

Sample Input #2

1
2

Sample Output #2

Bob

见题面 Input 部分

见题面 Output 部分