<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>

int dp[2001];
int ways[2001];
int rec(int level,vector<int>& nums){

    if(dp[level]!=-1) return dp[level];
    int ans = 0;
    for(int i=0;i<level;i++){
        if(nums[i] < nums[level]){
            if(ans < 1 + rec(i,nums)){
                ans = 1 + rec(i,nums);
                ways[level] = ways[i];
            }
            else if(ans == 1 + rec(i,nums)){
                ways[level] += ways[i];
            }
        }
    }
    return dp[level]=ans;
}
class Solution {
public:
    int findNumberOfLIS(vector<int>& nums) {
        memset(dp,-1,sizeof(dp));
        memset(ways,0,sizeof(ways));
        int n = nums.size();
        for (int i = 0; i < n; i++) {
            ways[i] = 1; 
        }
        int ans = 0;
        // int node = -1;
        
        for(int i=0;i<n;i++){
           ans = max(ans,rec(i,nums));
        }
        int final = 0;
        for(int i=0;i<n;i++){
            if(dp[i]==ans){
                final += ways[i];
            }
        }
        cout<<ans<<endl;
        return final;
    }
};
15500