You are given a 0-indexed array of positive integers nums. A triplet of three distinct indices (i, j, k) is called a single divisor triplet of nums if nums[i] + nums[j] + nums[k] is divisible by exactly one of nums[i], nums[j], or nums[k].

Return the number of single divisor triplets of nums.

 

Example 1:

Input: nums = [4,6,7,3,2]
Output: 12
Explanation:
The triplets (0, 3, 4), (0, 4, 3), (3, 0, 4), (3, 4, 0), (4, 0, 3), and (4, 3, 0) have the values of [4, 3, 2] (or a permutation of [4, 3, 2]).
4 + 3 + 2 = 9 which is only divisible by 3, so all such triplets are single divisor triplets.
The triplets (0, 2, 3), (0, 3, 2), (2, 0, 3), (2, 3, 0), (3, 0, 2), and (3, 2, 0) have the values of [4, 7, 3] (or a permutation of [4, 7, 3]).
4 + 7 + 3 = 14 which is only divisible by 7, so all such triplets are single divisor triplets.
There are 12 single divisor triplets in total.

Example 2:

Input: nums = [1,2,2]
Output: 6
Explanation:
The triplets (0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), and (2, 1, 0) have the values of [1, 2, 2] (or a permutation of [1, 2, 2]).
1 + 2 + 2 = 5 which is only divisible by 1, so all such triplets are single divisor triplets.
There are 6 single divisor triplets in total.

Example 3:

Input: nums = [1,1,1]
Output: 0
Explanation:
There are no single divisor triplets.
Note that (0, 1, 2) is not a single divisor triplet because nums[0] + nums[1] + nums[2] = 3 and 3 is divisible by nums[0], nums[1], and nums[2].

 

Constraints:

• 3 <= nums.length <= 105
• 1 <= nums[i] <= 100