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#!/usr/bin/env python3
# Challenge 146
#
# Consider the following Curious Fraction Tree:
#
#
# Curious Fraction Tree
#
#
# You are given a fraction, member of the tree created similar to the above sample.
#
# Write a script to find out the parent and grandparent of the given member.
#
# Example 1:
# Input: $member = '3/5';
# Output: parent = '3/2' and grandparent = '1/2'
# Example 2:
# Input: $member = '4/3';
# Output: parent = '1/3' and grandparent = '1/2'
#
# Solution:
# for node a/b, the children are a/(a+b) and (a+b)/b
import sys
def parent(a, b):
if a / b < 1: # a/(a+b)
parent_a = a
parent_b = abs(b - a)
else: # (a+b)/b
parent_a = abs(b - a)
parent_b = b
return parent_a, parent_b
input_value = sys.argv[1]
a, b = map(int, input_value.split('/'))
print(f"{a}/{b} -> ", end="")
a, b = parent(a, b)
print(f"{a}/{b} -> ", end="")
a, b = parent(a, b)
print(f"{a}/{b}")
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