Algorithms and Data Structures

# Check if a number is a power of 2 with a single bitwise operation

Given a positive integer `n`, you are asked to find out if it’s a power of 2. It’s possible to do that with a single bitwise operation. If we consider the bitwise representation of a number that’s a power of 2, then it has a single `1` in the representation and the rest are `0`s.
 2^n number Binary representation 8 1000 32 100000 128 10000000
 Random Number Binary representation 7 111 67 1000011 144 10010000
This can be seen from the definition of binary representation. Every position with a 1 corresponds to the addition of that power of 2 (67 = 1 + 2 + 0 + 0 + 0 + 0 + 64, 8 = 0 + 0 + 0 + 8). So, having a single `1` in the binary representation of a number means that there are no other powers of 2 in the sum other than that one. So, the problem becomes checking if there is only a single `1` in the binary representation of `n`.
An easy way of doing that is by doing a bitwise `&` of `n` and `n-1`. If the result is 0 ⇒ it’s a power of 2.
For any number that’s not a power of 2, the result of `n & (n-1)` will be different from 0:
• 7 & 6 = 111 & 110 = 110 (6)
• 67 & 66 = 1000011 & 1000010 = 1000010 (66)
• 144 & 143 = 10010000 & 10001111 = 10000000 (128)
Yet, for the powers of 2, it’s always 0:
• 8 & 7 = 1000 & 111 = 0
• 32 & 31 = 100000 & 11111 = 0
• 128 & 127 = 10000000 & 1111111 = 0
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Intuition When considering the numbers `n` and `n-1`, the most significant bit of those two is preserved only when the binary representation of `n` has other 1s other than the most significant bit. If `n` is a power of 2 ⇒ the binary representation has only a single 1, and thus when subtracting 1, `n-1` loses the most significant bit (it becomes 0 and the rest of the bits turn to 1). For other numbers (6, 67, 144, etc.) their binary representations contain several 1s. Therefore, when subtracting 1 from them, they don’t lose their most significant bits.

#### Input

The first line of the input contains a single integer `n` (2 ≤ n ≤
).

#### Output

The program should print `Yes` if `n` is a power of 2 and `No` otherwise.

#### Examples

 Input Output 8 Yes 17 No 2048 Yes

#### Constraints

Time limit: 0.2 seconds

Memory limit: 512 MB

Output limit: 1 MB