#!/usr/bin/env python
# coding=utf-8

"""243. Resilience
https://projecteuler.net/problem=243

A positive fraction whose numerator is less than its denominator is called a
proper fraction.  
For any denominator, d, there will be d−1 proper fractions; for example, with
d = 12:  
1/12 , 2/12 , 3/12 , 4/12 , 5/12 , 6/12 , 7/12 , 8/12 , 9/12 , 10/12 , 11/12 .

We shall call a fraction that cannot be cancelled down a _resilient fraction_.  
Furthermore we shall define the _resilience_ of a denominator,  R(d), to be
the ratio of its proper fractions that are resilient; for example, R(12) =
4/11 .  
In fact, d = 12 is the smallest denominator having a resilience R(d) < 4/10 .

Find the smallest denominator d, having a resilience R(d) < 15499/94744 .
"""
