The game “Back to Square 1” is played on a board that has *n* squares in a row and *n-1* probabilities. Players take turns playing. On their first turn, a player advances to square 1.After the first turn, if a player is on square *i* , the player advances to square *i* + 1 with probability *p(i)* , and returns to square 1 with probability 1-*p(i)* .The player is finished upon reaching square *n* .

**Task**

Write a program that determines the expected number of turns needed for a player to reach the final square.For example, consider the board below with *n* = 3 and *p(1)* = 0.5 and *p(2)* = 0.25. A player moves to square 1 on their first turn. With probability *p(1)* , they move to square 2 on their second turn, but with probability 1- *p(1)* , they remain on square 1. If they were lucky and made it to square 2 on their second turn, they advance to square 3 on their third turn with probability *p(2)* , but they would go back to square 1 with probability 1- *p(2)* . Thus, a really lucky player could finish is 3 turns. However, on average, it would take 13 turns for a player to make it to square 3.

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