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CSES Problem Set

Dice Probability


Task | Statistics


CSES - Dice ProbabilityCSES - Dice Probability

Time limit:1.00 s Memory limit:512 MB

You throw a dice $n$ times, and every throw produces an outcome between $1$ and $6$. What is the probability that the sum of outcomes is between $a$ and $b$?

Input

The only input line contains three integers $n$, $a$ and $b$.

Output

Print the probability rounded to six decimal places.

Constraints
Example

Input:
2 9 10

Output:
0.194444