Determine if a Binary Number is a Power of Two

You are given a string representing a binary number. Your task is to check whether the number is a power of two.

A number is a power of two if and only if its binary representation contains exactly one 1 bit. In mathematical notation, if \(s\) is the binary string, then the condition to be a power of two is:

$$\text{count}(1\text{'s in } s) = 1$$

For example:

• 10 represents 2 in decimal, which is \(2^1\) so the answer is True.
• 11 represents 3 in decimal, which is not a power of two so the answer is False.
• 10000 represents 16 in decimal, which is \(2^4\) so the answer is True.

The input is provided via standard input (stdin), and you should output the result via standard output (stdout).

inputFormat

The input consists of a single line containing a non-empty string \(s\) that represents a binary number. The string will only contain characters '0' and '1'.

Example:

1000

outputFormat

Output a single line with True if the binary string represents a power of two; otherwise, output False.

Example:

True

## sample

10

True