PIHEX2

All people use decimal system every day. For all of us the value of Pi is 3.141592653589793238462643383279....

But it is common to use the hexadecimal system in programming. The hexadecimal value of Pi is 3.243F6A8885A308D313198A2E037073....

In this problem for given value a, you should compute the digit that appears in hexadecimal representation of Pi at the a^th position after comma (for a=0 the answer is '3' - the only digit before comma, for a=1 the answer is '2' - the first digit after comma; see example to clarify).

Input

The first line of input contains single integer t - the number of test cases (1 ≤ t ≤ 20).

The second line of input contains t single-space separated integers a₁, a₂ ... a_t (0 ≤ a_i ≤ 1000000).

Output

The only line of output should contain t hexadecimal digits (use capital letters A-F), where i^th digit appears in Pi hexadecimal representation at a_i^th position.

Example

Input:

16
0 1 2 3 4 5 6 7 8 9 10 100 1000 10000 100000 1000000

Output:

3243F6A8885C3652