Given an integer array nums, return the number of longest increasing subsequences.

Notice that the sequence has to be strictly increasing.

 

Example 1:

Input: nums = [1,3,5,4,7]
Output: 2
Explanation: The two longest increasing subsequences are [1, 3, 4, 7] and [1, 3, 5, 7].

Example 2:

Input: nums = [2,2,2,2,2]
Output: 5
Explanation: The length of the longest increasing subsequence is 1, and there are 5 increasing subsequences of length 1, so output 5.

 

Constraints:

• 1 <= nums.length <= 2000
• -106 <= nums[i] <= 106
• The answer is guaranteed to fit inside a 32-bit integer.