Thank for providing $3$ hacks. (#11 ~ #13)

Problem Statement

Determine whether the input is a decimal/octal/hexadecimal integer or a decimal real number.

Ensure that if the input is a number, there is only one $0$ in front of the octal, and $0\text x$ in front of the hexadecimal, and all numbers have no redundant leading $0$.

Constraints

• Let $|a|$ represent the length of the string $a$, then $|s|\leq 1.004\times10^7$.
• $s$ is a number or string that meets the requirements of the topic or does not meet the requirements.

Input

The input is given from Standard Input in the following format:

$\color{#cccccc}\boxed{\color{white}{\large{|}}\color{black}s\color{white}{\large{|}}}$

Output

Print Yes if $s$ meets the requirements, and No otherwise.

Sample Input 1

1234567.98

Sample Output 1

Yes

Sample Input 2

0x123abc

Sample Output 2

Yes

Sample Input 3

-01243

Sample Output 3

Yes

Sample Input 4

1a2b3c

Sample Output 4

No