You are given a 1-indexed array nums of n integers.
A set of numbers is complete if the product of every pair of its elements is a perfect square.
\n\nFor a subset of the indices set {1, 2, ..., n} represented as {i1, i2, ..., ik}, we define its element-sum as: nums[i1] + nums[i2] + ... + nums[ik].
Return the maximum element-sum of a complete subset of the indices set {1, 2, ..., n}.
A perfect square is a number that can be expressed as the product of an integer by itself.
\n\n\n
Example 1:
\n\n\nInput: nums = [8,7,3,5,7,2,4,9]\nOutput: 16\nExplanation: Apart from the subsets consisting of a single index, there are two other complete subsets of indices: {1,4} and {2,8}.\nThe sum of the elements corresponding to indices 1 and 4 is equal to nums[1] + nums[4] = 8 + 5 = 13.\nThe sum of the elements corresponding to indices 2 and 8 is equal to nums[2] + nums[8] = 7 + 9 = 16.\nHence, the maximum element-sum of a complete subset of indices is 16.\n\n\nExample 2:
\n\n\nInput: nums = [5,10,3,10,1,13,7,9,4]\nOutput: 19\nExplanation: Apart from the subsets consisting of a single index, there are four other complete subsets of indices: {1,4}, {1,9}, {2,8}, {4,9}, and {1,4,9}.\nThe sum of the elements corresponding to indices 1 and 4 is equal to nums[1] + nums[4] = 5 + 10 = 15.\nThe sum of the elements corresponding to indices 1 and 9 is equal to nums[1] + nums[9] = 5 + 4 = 9.\nThe sum of the elements corresponding to indices 2 and 8 is equal to nums[2] + nums[8] = 10 + 9 = 19.\nThe sum of the elements corresponding to indices 4 and 9 is equal to nums[4] + nums[9] = 10 + 4 = 14.\nThe sum of the elements corresponding to indices 1, 4, and 9 is equal to nums[1] + nums[4] + nums[9] = 5 + 10 + 4 = 19.\nHence, the maximum element-sum of a complete subset of indices is 19.\n\n\n\n
Constraints:
\n\n1 <= n == nums.length <= 1041 <= nums[i] <= 109P(x) be the product of all prime numbers p such that p divides x, and there exists an odd k such that p^k divides x but p^(k+1) does not.",
"If P(nums[i]) = P(nums[j]), nums[i] and nums[j] can be grouped together.",
"Pick the group with the largest sum."
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