3395 - Subsequences with a Unique Middle Mode I.

Hard

Given an integer array nums, find the number of subsequences of size 5 of nums with a unique middle mode.

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

A mode of a sequence of numbers is defined as the element that appears the maximum number of times in the sequence.

A sequence of numbers contains a unique mode if it has only one mode.

A sequence of numbers seq of size 5 contains a unique middle mode if the middle element (seq[2]) is a unique mode.

A subsequence is a non-empty array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.

Example 1:

Input: nums = 1,1,1,1,1,1

Output: 6

Explanation:

[1, 1, 1, 1, 1] is the only subsequence of size 5 that can be formed, and it has a unique middle mode of 1. This subsequence can be formed in 6 different ways, so the output is 6.

Example 2:

Input: nums = 1,2,2,3,3,4

Output: 4

Explanation:

[1, 2, 2, 3, 4] and [1, 2, 3, 3, 4] each have a unique middle mode because the number at index 2 has the greatest frequency in the subsequence. [1, 2, 2, 3, 3] does not have a unique middle mode because 2 and 3 appear twice.

Example 3:

Input: nums = 0,1,2,3,4,5,6,7,8

Output: 0

Explanation:

There is no subsequence of length 5 with a unique middle mode.

Constraints:

• 5 <= nums.length <= 1000

• <code>-10⁹<= numsi<= 10⁹</code>