|Elly is not a big fan of mathematical constants. Most of them are infinite, and therefore hard to memorize. Fractions, on the other hand, are often easier to remember and can provide good approximations. For example, 22/7 = 3.1428... is one way to approximate Pi. Unfortunately, it's only accurate to 2 places after the decimal point, so it doesn't help at all. A slightly better example is 355/113 = 3.14159292... which is correct up to 6 digits after the decimal point.|
Elly understands that working with infinite decimal fractions is going to be very difficult, so she first wants to find a good way to approximate floating point numbers with decimal representations that are finite. Your task is to help her in this mission. You will be given a String number containing the decimal representation of a non-negative fraction strictly less than 1. There will be exactly 6 digits after the decimal point in number (trailing zeros are possible and significant). More precisely, number will be formatted "0.dddddd" (quotes for clarity) where each d is a decimal digit ('0'-'9').
Given a fraction F = A/B, where 0 <= A < B, its quality of approximation with respect to number is calculated as follows:
|-||maxDen will be between 1 and 1000, inclusive.|
|-||number will contain exactly 8 characters.|
|-||number will consist of a digit '0', followed by a period ('.'), followed by exactly six digits ('0'-'9').|