The Long Way Home Emilia is playing a board game where each player needs to move their game piece

along the black roads from the beach in the bottom-left corner to the house in

the top-right corner. The black dots represent intersections where roads meet.

In each turn a player is allowed to move their piece along a road until it reaches

an intersection. Then it’s another player’s turn.

After Emilia finished the game, she realized that at every intersection she had

turned either left or right; she never continued straight along the direction she

came from in her previous turn. As well, she never went along the same part of a

road more than once.

What is the fewest number of turns Emilia could have had during the game?