Equations of Mathematical Magic

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 ⊕ x) - x = 0 for some given a, where ⊕ 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 ≤ t ≤ 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 ... x_2 x_1 x_0 and y_k ... 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 ⊕ y be the result of the XOR operation of x and y. Then r is defined as r_k ... r_2 r_1 r_0 where:

$$$ r_i = \left\{ \begin{aligned} 1, ~ if ~ x_i ≠ y_i \\\ 0, ~ if ~ x_i = y_i \end{aligned} \right. $ $$

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.

inputFormat

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 ≤ t ≤ 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.

outputFormat

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 ... x_2 x_1 x_0 and y_k ... 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 ⊕ y be the result of the XOR operation of x and y. Then r is defined as r_k ... r_2 r_1 r_0 where:

$$$ r_i = \left\{ \begin{aligned} 1, ~ if ~ x_i ≠ y_i \\\ 0, ~ if ~ x_i = y_i \end{aligned} \right. $ $$

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.

样例

3
0
2
1073741823

1
2
1073741824

</p>