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