Dice Probability

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