Maximum Perfect Square Adjacent Pair Weight

You have lost your memory, and the Singer took it away. However, before leaving, the Singer told you that your memory contained a permutation of all integers from (l) to (r), and that this permutation has the maximum weight among all possible permutations.

The weight of a sequence is defined as the number of adjacent pairs ((a_i, a_{i+1})) such that the product (a_i \cdot a_{i+1}) is a perfect square, i.e., there exists an integer (k) satisfying (a_i \cdot a_{i+1} = k^2). It can be shown that (a_i \cdot a_{i+1}) is a perfect square if and only if the two numbers have the same square-free part.

Thus, to maximize the weight, one should group together numbers that have identical square-free parts. In any arrangement, if a group has (k) numbers sharing the same square-free part, they can contribute up to (k-1) to the weight. Since the permutation consists of every integer from (l) to (r) exactly once, the maximum weight equals ((r - l + 1) - G), where (G) is the number of distinct square-free parts among the numbers in ([l, r]).

Your task is to compute and output this maximum weight.

inputFormat

The input consists of a single line containing two integers (l) and (r) (with (l \le r)), separated by a space.

outputFormat

Output a single integer representing the maximum weight of a permutation of all integers from (l) to (r), i.e. [ \text{Maximum Weight} = (r - l + 1) - G, ] where (G) is the number of distinct square-free parts in the interval.

sample

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