CF1497E2 Square-free division (hard version)
Description
This is the hard version of the problem. The only difference is that in this version $ 0 \leq k \leq 20 $ .
There is an array $ a_1, a_2, \ldots, a_n $ of $ n $ positive integers. You should divide it into a minimal number of continuous segments, such that in each segment there are no two numbers (on different positions), whose product is a perfect square.
Moreover, it is allowed to do at most $ k $ such operations before the division: choose a number in the array and change its value to any positive integer.
What is the minimum number of continuous segments you should use if you will make changes optimally?
Input Format
N/A
Output Format
N/A
Explanation/Hint
In the first test case it is possible to change the array this way: $ [\underline{3}, 6, 2, 4, \underline{5}] $ (changed elements are underlined). After that the array does not need to be divided, so the answer is $ 1 $ .
In the second test case it is possible to change the array this way: $ [6, 2, \underline{3}, 8, 9, \underline{5}, 3, 6, \underline{10}, \underline{11}, 7] $ . After that such division is optimal:
- $ [6, 2, 3] $
- $ [8, 9, 5, 3, 6, 10, 11, 7] $