Phoenix and Balance

2000ms

262144K

Description:

Phoenix has $$$n$$$ coins with weights $$$2^1, 2^2, \dots, 2^n$$$. He knows that $$$n$$$ is even.

He wants to split the coins into two piles such that each pile has exactly $$$\frac{n}{2}$$$ coins and the difference of weights between the two piles is minimized. Formally, let $$$a$$$ denote the sum of weights in the first pile, and $$$b$$$ denote the sum of weights in the second pile. Help Phoenix minimize $$$|a-b|$$$, the absolute value of $$$a-b$$$.

Input:

The input consists of multiple test cases. The first line contains an integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases.

The first line of each test case contains an integer $$$n$$$ ($$$2 \le n \le 30$$$; $$$n$$$ is even) — the number of coins that Phoenix has.

Output:

For each test case, output one integer — the minimum possible difference of weights between the two piles.

Sample Input:

2
2
4

Sample Output:

2
6

Note:

In the first test case, Phoenix has two coins with weights $$$2$$$ and $$$4$$$. No matter how he divides the coins, the difference will be $$$4-2=2$$$.

In the second test case, Phoenix has four coins of weight $$$2$$$, $$$4$$$, $$$8$$$, and $$$16$$$. It is optimal for Phoenix to place coins with weights $$$2$$$ and $$$16$$$ in one pile, and coins with weights $$$4$$$ and $$$8$$$ in another pile. The difference is $$$(2+16)-(4+8)=6$$$.

Informação

Provedor Codeforces

Código CF1348A