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".