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# Now posted: Presumptuous base conversion

Take an input string representing a number and convert it to decimal (base 10). However, the base of the input is not specified. Assume the input is in the smallest base for which its digits are valid.

## Input

• The input consists only of characters from 0123456789ABCDEF where A to F represent the decimal numbers 10 to 15
• The input will always contain at least one character (it will never be empty)
• The input will sometimes have one or more leading zeroes

## Output

• If the highest digit in the input is represented by N, then the input is to be treated as being in base N+1
• For this challenge, the letters A to F count as "digits". So if the highest digit in the input is B, which represents 11, then the input is in base 12
• In particular, if the highest digit in the input is 0, then the input is to be treated as being in base 1 (unary), so the output is the number of digits in the input
• Apart from inputs in base 1 (unary), leading zeroes make no difference to the output. Both "11" and "000011" lead to output "3"

## Examples

• If the input is 453 then the highest digit is 5, so the input is in base 6. The output is 177, calculated as 4*6*6 + 5*6 + 3
• If the input is 000 then the highest digit is 0 so the input is in base 1 (unary). The output is 3, which is simply the length of the unary input

## Test cases

Test cases are in the form input : output

0 : 1
1 : 1
9 : 9
A : 10
E : 14
F : 15
00 : 2
01 : 1
10 : 2
11 : 3
02 : 2
20 : 6
22 : 8
65 : 47
99 : 99
AA : 120
B8 : 140
000 : 3
00F : 15
0D0 : 182
C00 : 2028
123 : 27
ABC : 1845
777 : 511
453 : 177

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