Problem B
Monopoly

Doris is playing monopoly with her friends, and it is now her turn to roll the dice. In standard monopoly you roll two $6$-sided dice, and then walk the same number of steps as the sum of the two dice. From her current position, she will end up on her opponents’ hotels if the sum is equal to one of the integers $A_1, \dots , A_ N$. What is the probability that she will end up on one of her opponents’ hotels during her current turn? You do not have to consider the rule about rerolling if both dice show the same number or any other rule from monopoly.

Input

The first line consists of an integer $N$ ($1 \leq N \leq 11$), the number of hotels the opponents own. The second line consists of $N$ integers $A_1, \dots , A_ N$ ($2 \leq A_1 < \dots < A_ N \leq 12$), the distances to each of the opponents’ $N$ hotels.

Output

Output a decimal, the probability that the sum of the two dice is one of the numbers $A_1, \dots , A_ N$. Your answer will be considered correct if its absolute error does not exceed $10^{-4}$.

Grading

Your solution will be tested on two test-case groups. To receive points for a group, your solution must correctly solve every test-case in the group.

1
7

0.16666666666666666

2
2 12

0.05555555555555555

11
2 3 4 5 6 7 8 9 10 11 12

1.0