Your task is to evaluate  the following series for a given n

2^n - ((n-1)C(1))*2^(n-2)  + ((n-2)C(2))*2^(n-4) - ((n-3)C(3))*2^(n-6)+ ...

(n)C(r) denotes n choose r.

Power of 2 is always non-negative.(i.e. series terminates when either power of 2 goes negative or combinatorics becomes undefined.)

Input

First line of input contains the number of test cases (t <= 100000), then follows t lines, each containing the value of n (n <= 100000.)

Output

You should output t lines, ith line contains answer of the ith test case

Example

Input:
2
1
2

Output:
2
3 

Click here to see my set of problems at Spoj.