OR equal XOR

Problem Description

You are given an integer A. Find the number of ordered pairs (x, y) such that 0 ≤ x, y < 2^A and they satisfy the following condition-

(x ^ y) = (x | y).

In other words, the bitwise XOR of both these numbers is equal to the bitwise OR of these numbers. Since the answer can be large, calculate it modulo 10⁹ + 7.

Problem Constraints

0 <= A <= 10⁵

Input Format

The first and only argument contains an integer A.

Output Format

Return a single integer denoting the answer.

Example Input

Input 1:

Input 2:

Example Output

Output 1:

Output 2:

Example Explanation

Explanation 1:

  Valid pair - (0, 0)

Explanation 2:

  Valid pairs - (0, 0), (0, 1), (1, 0)

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.

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Hints

Hint 1
Solution Approach
Complete Solution

OR equal XOR

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