Editing 2016 Jan Platinum Problem 3 Lights Out (section)

== Problem ==

In the "Lights Out" problem, Farmer John's cows are having a party and Bessie is tasked with turning off the barn lights once the party is over. Unfortunately, the cows have installed a complex network of switches. There are N (2 <= N <= 200) switches in the barn numbered from 1 to N and M (1 <= M <= 10,000) connections between them. Each connection is a one-way connection from one switch to another switch and if a connection from switch A to switch B is activated, it toggles the state of switch B (if it is off, it turns on and if it is on, it turns off). The cows have guaranteed that from any switch, there is a unique way to reach every other switch.

Bessie begins at switch 1 and wants to turn off all the switches. She can only leave once all the switches are turned off. At the start, all switches are on. The goal of the problem is to figure out the minimum number of times Bessie needs to traverse each connection such that she ends at switch 1 and all the switches are off.