You are given a 1**-indexed** array nums. Your task is to select a complete subset from nums where every pair of selected indices multiplied is a perfect square,. i. e. if you select aᵢ and aⱼ, i * j must be a perfect square.

Return the sum of the complete subset with the maximum sum.

Examples

Example 1

Input:  nums = [8,7,3,5,7,2,4,9]
Output: 16

We select elements at indices 2 and 8 and 2 * 8 is a perfect square.

Example 2

Input:  nums = [8,10,3,8,1,13,7,9,4]
Output: 20

We select elements at indices 1, 4, and 9. 1 * 4, 1 * 9, 4 * 9 are perfect squares.

Constraints

• 1 <= n == nums.length <= 10⁴
• 1 <= nums[i] <= 10⁹