487. Is Valid Number

0

Hard

You are given a string s ( a number) . You have to find out that the given number is valid or not .

A valid number can be split up into these components (in order):

1.A decimal number or an integer.

2.(Optional) An 'e' or 'E', followed by an integer.

A decimal number can be split up into these components (in order):

1.(Optional) A sign character (either '+' or '-').

One of the following formats:

* One or more digits, followed by a dot '.'.

* One or more digits, followed by a dot '.', followed by one or more digits. * A dot '.', followed by one or more digits.

An integer can be split up into these components (in order):

* (Optional) A sign character (either '+' or '-'). * One or more digits.

For example, all the following are valid numbers:

["2", "0089", "-0.1", "+3.14", "4.", "-.9", "2e10", "-90E3", "3e+7", "+6e-1", "53.5e93", "-123.456e789"],

while the following are not valid numbers:

["abc", "1a", "1e", "e3", "99e2.5", "--6", "-+3", "95a54e53"]. Given a string s, return YES if s is a valid number.

A valid number can be split up into these components (in order):

1.A decimal number or an integer.

2.(Optional) An 'e' or 'E', followed by an integer.

A decimal number can be split up into these components (in order):

1.(Optional) A sign character (either '+' or '-').

One of the following formats:

* One or more digits, followed by a dot '.'.

* One or more digits, followed by a dot '.', followed by one or more digits. * A dot '.', followed by one or more digits.

An integer can be split up into these components (in order):

* (Optional) A sign character (either '+' or '-'). * One or more digits.

For example, all the following are valid numbers:

["2", "0089", "-0.1", "+3.14", "4.", "-.9", "2e10", "-90E3", "3e+7", "+6e-1", "53.5e93", "-123.456e789"],

while the following are not valid numbers:

["abc", "1a", "1e", "e3", "99e2.5", "--6", "-+3", "95a54e53"]. Given a string s, return YES if s is a valid number.

Input Format

Single Line consists of a string s.

Output Format

Print "YES" or "NO"

Example

Input

123.45

Output

YES

Constraints

1 <= s.length <=10000

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