The icosian game was created by Ireland’s greatest mathematician William Rowan Hamilton in 1857 and consists of the following graph :

The aim of the game was to determine a path that passes through all of the vertices once and only once, and then returns to the starting point. Is it possible to find such a route in the above graph? Submit 1 for 'Yes' and 0 for 'No'.

The Answer is an integer. Just put the number without any decimal places.