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  1. Practice
  2. Algorithms
  3. Bit Manipulation
  4. The Great XOR

The Great XOR

Given a long integer , count the number of values of satisfying the following conditions:

where and are long integers and is the bitwise XOR operator.

You are given queries, and each query is in the form of a long integer denoting . For each query, print the total number of values of satisfying the conditions above on a new line.

For example, you are given the value . Condition requires that . The following tests are run:




We find that there are values meeting the first condition: and .

Function Description

Complete the theGreatXor function in the editor below. It should return an integer that represents the number of values satisfying the constraints.

theGreatXor has the following parameter(s):

  • x: an integer

Input Format

The first line contains an integer , the number of queries.
Each of the next lines contains a long integer describing the value of for a query.

Constraints

Subtasks

For of the maximum score:

Output Format

For each query, print the number of values of satisfying the given conditions on a new line.

Sample Input 0

2
2
10

Sample Output 0

1
5

Explanation 0

We perform the following queries:

  1. For the only value of satisfying is . This also satisfies our other condition, as and . Because we have one valid and there are no more values to check, we print on a new line.

  2. For , the following values of satisfy our conditions:





    There are five valid values of .

Sample Input 1

2
5
100

Sample Output 1

2
27

Explanation 1

In the first case:


In the second case, the first 10 values are: