Task

Consider two following representations of a non-negative integer:

A simple decimal integer, constructed of a non-empty sequence of digits from 0 to 9;

An integer with at least one digit in a base from 2 to 16 (inclusive), enclosed between # characters, and preceded by the base, which can only be a number between 2 and 16 in the first representation. For digits from 10 to 15 characters a, b, ..., f and A, B, ..., F are used.

Additionally, both representations may contain underscore (_) characters; they are used only as separators for improving legibility of numbers and can be ignored while processing a number.

Your task is to determine whether the given string is a valid integer representation.

Note: this is how integer numbers are represented in the programming language Ada.

Example

For line = "123_456_789", the output should be true;

For line = "16#123abc#", the output should be true;

For line = "10#123abc#", the output should be false;

For line = "10#10#123ABC#", the output should be false;

For line = "10#0#", the output should be true;

For line = "10##", the output should be false.

Input/Output

• [input] string line

A non-empty string.

• [output] a boolean value

true if line is a valid integer representation, false otherwise.