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 (rounding half to even).

Constraints

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

Example

Input:

2 9 10

Output:

0.194444