There are $N$ cards, where $N = 2k + 1$ is an odd integer $\geq 3$.

Also, there are two arrays $A = [a_1, a_2, ... , a_N]$ and $H = [h_1, h_2, ... , h_N]$.

Here $a_i$ and $h_i$ represent the attack point and the health point of the $i$th card, respectively.

Assume that Alice choose $k$ cards first, and then Bob accepts the other $k + 1$ cards automatically.

Let $h_a$ and $h_b$ be the minimal health points of Alice and Bob, respectively.

Suppose that the total power of Alice is obtained by multiplyng $h_a$ by the sum of the attack points of Alice's cards.

Similarly, the power of Bob is obtained by multiplyng $h_b$ by the sum of the attack points of his cards.

Then, determine the winner if both players play optimally.

Constraints

• $1 \leq T \leq 1000$
• $3 \leq N \leq 10^5$
• $1 \leq a_i \leq 10^5$
• $1 \leq h_i \leq 10^5$

•  The sum of $N$ across all test cases does not exceed $2 \cdot 10 ^ 5$.

Input Format

• The first line contains a single integer $T$ —- the number of test cases.
• For each testcase:
  • The first line contains one odd integer $N$ —- the length of the arrays.
  • The second line contains $N$ positive integers $a_1, a_2, ... , a_N$.

  • The third line contains $N$ positive integers $h_1, h_2, ... , h_N$.

• The sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.

Output Format

• For each testcase, output a single line:
  • "Alice" if Alice wins with the optimal play.
  • "Bob" if Bob wins with the optimal play.
  • Otherwise, output "Tie".