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 $b$ ?

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

• $1 \le n \le 100$
• $1 \le a \le b \le 6n$

Print the probability rounded to six decimal places (rounding half to even).