Arithmetic Game

Problem Description

Alice and Bob are very bored, so they decided to play a short game on a piece of paper. First, they write down $n$ $(n \ge 3)$ numbers $a_1, a_2, ..., a_n$. Then they calculate the score, which is the arithmetic mean of the list and write it at the edge of the paper so they don't forget.

Alice and Bob each have exactly one turn; Alice goes first. On each turn, a player chooses any element and removes it from the list. Once both players have finished their turns, the score is calculated again with the new list. If the final score is less than the initial score, Alice wins; if it remains the same, the game ends in a Tie; otherwise, Bob wins.

If Alice and Bob play optimally, output the result of the game.

• Arithmetic mean of a list $a$ of size $n$ is calculated as: $\lfloor \frac{a_1 + a_2 + \dots + a_n}{n} \rfloor$

Input format

The first line contains $n$ $(3 \le n \le 10^6)$ --- the number of elements in $a$.

The next line contains $n$ numbers $a_1, a_2, ..., a_n$ $$ --- the initial list before any changes.

Output format

For each test, output on a separate line:

• Alice, if the final score is less than the initial score.
• Tie, if the final score will be the same as the initial score.
• Bob, if the final score is greater than the initial score.

Scoring system

4
1 2 3 4

Tie

3
76 99 72

Alice