3583 - Count Special Triplets.

Medium

You are given an integer array nums.

A special triplet is defined as a triplet of indices (i, j, k) such that:

• 0 <= i < j < k < n, where n = nums.length

• nums[i] == nums[j] * 2

• nums[k] == nums[j] * 2

Return the total number of special triplets in the array.

Since the answer may be large, return it modulo <code>10⁹ + 7</code>.

Example 1:

Input: nums = 6,3,6

Output: 1

Explanation:

The only special triplet is (i, j, k) = (0, 1, 2), where:

• nums[0] = 6, nums[1] = 3, nums[2] = 6

• nums[0] = nums[1] * 2 = 3 * 2 = 6

• nums[2] = nums[1] * 2 = 3 * 2 = 6

Example 2:

Input: nums = 0,1,0,0

Output: 1

Explanation:

The only special triplet is (i, j, k) = (0, 2, 3), where:

• nums[0] = 0, nums[2] = 0, nums[3] = 0

• nums[0] = nums[2] * 2 = 0 * 2 = 0

• nums[3] = nums[2] * 2 = 0 * 2 = 0

Example 3:

Input: nums = 8,4,2,8,4

Output: 2

Explanation:

There are exactly two special triplets:

• (i, j, k) = (0, 1, 3)

• (i, j, k) = (1, 2, 4)

Constraints:

• <code>3 <= n == nums.length <= 10⁵</code>

• <code>0 <= numsi<= 10⁵</code>