# Solution of;
# Project Euler Problem 57: Square root convergents
# https://projecteuler.net/problem=57
# 
# It is possible to show that the square root of two can be expressed as an 
# infinite continued fraction. $\sqrt 2 =1+ \frac 1 {2+ \frac 1 {2 +\frac 1 
# {2+ \dots}}}$By expanding this for the first four iterations, we get:$1 + 
# \frac 1 2 = \frac 32 = 1. 5$$1 + \frac 1 {2 + \frac 1 2} = \frac 7 5 = 1. 
# 4$$1 + \frac 1 {2 + \frac 1 {2+\frac 1 2}} = \frac {17}{12} = 1. 41666 
# \dots$$1 + \frac 1 {2 + \frac 1 {2+\frac 1 {2+\frac 1 2}}} = \frac {41}{29} 
# = 1. 41379 \dots$The next three expansions are $\frac {99}{70}$, $\frac 
# {239}{169}$, and $\frac {577}{408}$, but the eighth expansion, $\frac 
# {1393}{985}$, is the first example where the number of digits in the 
# numerator exceeds the number of digits in the denominator. In the first 
# one-thousand expansions, how many fractions contain a numerator with more 
# digits than the denominator?
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 57
    timed.caller(dummy, n, i, prob_id)
