Source

This problem is adapted from Long Long OJ. All rights reserved.

Description

Determine whether the input is an octal integer/hexadecimal integer/decimal real number (possibly negative).

If the input is a number:

• There is a $0$ before octal.
• There is a $\text{0x}$ before hexadecimal.
• The end of decimal real numbers is allowed to have zeros.
• Numbers equal to $0$ are not allowed to have a negative sign.
• All numbers have no redundant leading zeros or negative signs.
• Decimal real numbers less than $1$ are not allowed to omit the integer part ($0$).

It is guarateed that:

• Input is not empty.
• The input length does not exceed $1.004 \times 10^7$.
• Input only contains negative signs, numbers, and lowercase letters.

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.

Samples

1234567.98

Yes

0x123abc

Yes

-01243

Yes

1a2b3c

No