Perfect Triples

Consider the infinite sequence s of positive integers, created by repeating the following steps:

1. Find the lexicographically smallest triple of positive integers (a, b, c) such that * a ⊕ b ⊕ c = 0, where ⊕ denotes the bitwise XOR operation. * a, b, c are not in s. Here triple of integers (a_1, b_1, c_1) is considered to be lexicographically smaller than triple (a_2, b_2, c_2) if sequence [a_1, b_1, c_1] is lexicographically smaller than sequence [a_2, b_2, c_2].
2. Append a, b, c to s in this order.
3. Go back to the first step.

You have integer n. Find the n-th element of s.

You have to answer t independent test cases.

A sequence a is lexicographically smaller than a sequence b if in the first position where a and b differ, the sequence a has a smaller element than the corresponding element in b.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.

Each of the next t lines contains a single integer n (1≤ n ≤ 10^{16}) — the position of the element you want to know.

Output

In each of the t lines, output the answer to the corresponding test case.

Example

Input

9 1 2 3 4 5 6 7 8 9

Output

1 2 3 4 8 12 5 10 15

Note

The first elements of s are 1, 2, 3, 4, 8, 12, 5, 10, 15, ...

inputFormat

Input

The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases.

Each of the next t lines contains a single integer n (1≤ n ≤ 10^{16}) — the position of the element you want to know.

outputFormat

Output

In each of the t lines, output the answer to the corresponding test case.

Example

Input

9 1 2 3 4 5 6 7 8 9

Output

1 2 3 4 8 12 5 10 15

Note

The first elements of s are 1, 2, 3, 4, 8, 12, 5, 10, 15, ...

样例

9
1
2
3
4
5
6
7
8
9

1
2
3
4
8
12
5
10
15

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