CSES - 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
  • $1 \le n \le 100$
  • $1 \le a \le b \le 6n$
Example

Input:
2 9 10

Output:
0.194444