Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

B. Equations of Mathematical Magic

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputColossal! — exclaimed Hawk-nose. — A programmer! That's exactly what we are looking for.

Arkadi and Boris Strugatsky. Monday starts on Saturday

Reading 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.

Input

Each 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.

Output

For 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.

Example

Input

3

0

2

1073741823

Output

1

2

1073741824

Note

Let'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 $$$x = 2$$$.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jan/20/2020 02:26:58 (h3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|