# CF1064B Equations of Mathematical Magic

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## 题目描述

给出 $a$，判断方程 $a-(a \oplus x)-x=0$ 的解的个数。（其中 $\oplus$ 为异或）

## 输入格式

第一行是数据组数 $t$，接下来 $t$ 行每行输入一个整数 $a$。

## 输出格式

对于每组数据，输出对应的答案。

## 题目描述

Colossal! — 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.

## 输入输出格式

输入格式：

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.

输出格式：

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.

## 输入输出样例

输入样例#1： 复制
3
0
2
1073741823

输出样例#1： 复制
1
2
1073741824


## 说明

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. </p><p>For the first value of the parameter, only x = 0 is a solution of the equation.</p><p>For the second value of the parameter, solutions are x = 0 and x = 2.

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