Fermat's Last Theorem states that for $n > 2$, the Diophantine equation $a^n + b^n = c^n$ has no positive integer solutions. For example, $a^3 + b^3 = c^3$ has no positive integer solutions. To liven things up, let's consider a humorous version: we change the equation to $a^3 + b^3 = c$, which then has solutions, such as $a=4, b=9, c=79$, where $4^3 + 9^3 = 793$.
Given two integers $x$ and $y$, find the number of integer solutions satisfying $x \le a, b, c \le y$.
Input
The input contains at most 10 test cases. Each test case contains two integers $x, y$ ($1 \le x, y \le 10^8$).
Output
For each test case, output the number of solutions.
Examples
Input 1
1 10 1 20 123 456789
Output 1
Case 1: 0 Case 2: 2 Case 3: 16