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Number of Squareful Arrays

An array is squareful if the sum of every pair of adjacent elements is a perfect square.

An array is squareful if the sum of every pair of adjacent elements is a perfect square.

Given an integer array nums, return the number of permutations of nums that are squareful.

Two permutations perm1 and perm2 are different if there is some index i such that perm1[i] != perm2[i].

Number of Squareful Arrays diagram

Example 1

Input: nums = [1,17,8]

Output: 2

Explanation: [1,8,17] and [17,8,1] are the valid permutations.

Example 2

Input: nums = [2,2,2]

Output: 1

Constraints

  • 1 <= nums.length <= 12
  • 0 <= nums[i] <= 10^9

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