<p>Given an integer array&nbsp;<code>nums</code>, return <em>the number of longest increasing subsequences.</em></p>

<p><strong>Notice</strong> that the sequence has to be <strong>strictly</strong> increasing.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

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

<p><strong class="example">Example 2:</strong></p>

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

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 2000</code></li>
	<li><code>-10<sup>6</sup> &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>
	<li>The answer is guaranteed to fit inside a 32-bit integer.</li>
</ul>

class Solution:
 def findNumberOfLIS(self, nums: List[int]) -> int:

    if not nums:
        return 0
    
    n = len(nums)
    lengths = [1] * n  
    counts = [1] * n  
    
    for i in range(n):
        for j in range(i):
            if nums[j] < nums[i]:
                if lengths[j] + 1 > lengths[i]:
                    lengths[i] = lengths[j] + 1
                    counts[i] = counts[j]
                elif lengths[j] + 1 == lengths[i]:
                    counts[i] += counts[j]
    
   
    max_length = max(lengths)
    
  
    return sum(count for length, count in zip(lengths, counts) if length == max_length)
        
16300