B. Equations of Mathematical Magictime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputColossal! — exclaimed Hawk-nose. — A programmer! That's exactly what we are looking for.Arkadi and Boris Strugatsky. Monday starts on SaturdayReading the book "Equations of Mathematical Magic" Roman Oira-Oira and Cristobal Junta found an interesting equation: a - (a \oplus x) - x = 0 for some given a, where \oplus stands for a bitwise exclusive or (XOR) of two integers (this operation is denoted as ^ or xor in many modern programming languages). Oira-Oira quickly found some x, which is the solution of the equation, but Cristobal Junta decided that Oira-Oira's result is not interesting enough, so he asked his colleague how many non-negative solutions of this equation exist. This task turned out to be too difficult for Oira-Oira, so he asks you to help.InputEach test contains several possible values of a and your task is to find the number of equation's solution for each of them. The first line contains an integer t (1 \le t \le 1000) — the number of these values.The following t lines contain the values of parameter a, each value is an integer from 0 to 2^{30} - 1 inclusive.OutputFor each value of a print exactly one integer — the number of non-negative solutions of the equation for the given value of the parameter. Print answers in the same order as values of a appear in the input.One can show that the number of solutions is always finite.ExampleInput3021073741823Output121073741824NoteLet's define the bitwise exclusive OR (XOR) operation. Given two integers x and y, consider their binary representations (possibly with leading zeroes): x_k \dots x_2 x_1 x_0 and y_k \dots y_2 y_1 y_0. Here, x_i is the i-th bit of the number x and y_i is the i-th bit of the number y. Let r = x \oplus y be the result of the XOR operation of x and y. Then r is defined as r_k \dots r_2 r_1 r_0 where: r_i = \left\{ \begin{aligned} 1, ~ \text{if} ~ x_i \ne y_i \\ 0, ~ \text{if} ~ x_i = y_i \end{aligned} \right. For the first value of the parameter, only x = 0 is a solution of the equation.For the second value of the parameter, solutions are x = 0 and x = 2.
Input3021073741823
Output121073741824
['math', '*1200']