<p>There are <code>n</code> soldiers standing in a line. Each soldier is assigned a <strong>unique</strong> <code>rating</code> value.</p>

<p>You have to form a team of 3 soldiers amongst them under the following rules:</p>

<ul>
	<li>Choose 3 soldiers with index (<code>i</code>, <code>j</code>, <code>k</code>) with rating (<code>rating[i]</code>, <code>rating[j]</code>, <code>rating[k]</code>).</li>
	<li>A team is valid if: (<code>rating[i] &lt; rating[j] &lt; rating[k]</code>) or (<code>rating[i] &gt; rating[j] &gt; rating[k]</code>) where (<code>0 &lt;= i &lt; j &lt; k &lt; n</code>).</li>
</ul>

<p>Return the number of teams you can form given the conditions. (soldiers can be part of multiple teams).</p>

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

<pre>
<strong>Input:</strong> rating = [2,5,3,4,1]
<strong>Output:</strong> 3
<strong>Explanation:</strong> We can form three teams given the conditions. (2,3,4), (5,4,1), (5,3,1). 
</pre>

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

<pre>
<strong>Input:</strong> rating = [2,1,3]
<strong>Output:</strong> 0
<strong>Explanation:</strong> We can&#39;t form any team given the conditions.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> rating = [1,2,3,4]
<strong>Output:</strong> 4
</pre>

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

<ul>
	<li><code>n == rating.length</code></li>
	<li><code>3 &lt;= n &lt;= 1000</code></li>
	<li><code>1 &lt;= rating[i] &lt;= 10<sup>5</sup></code></li>
	<li>All the integers in <code>rating</code> are <strong>unique</strong>.</li>
</ul>

class Solution {
public:
    // vector<vector<int>> dp(1001, vector<int>(1001, -1));
    int dp[1001][1001];
    int ans=0;
    int LIS(vector<int> & rating, int i, int prev)
    {
        if(i==rating.size())
            return 0;
        if(dp[i][prev+1]!=-1)
            return dp[i][prev+1];
        
        int take = 0;
        if(prev==-1 || rating[prev]<rating[i])
        {  
           
            take = 1+LIS(rating, i+1, i);
        }
        if(take>2)
            ans++;
        
        int notTake = LIS(rating, i+1, prev);
        

        return dp[i][prev+1] = max(take, notTake);
    }
    int numTeams(vector<int>& rating) {
        
       int n = rating.size();
       int ans=0;

       for(int i=1; i<n-1; i++)
       {
            int lefti = 0;
            int leftd = 0;

            for(int j=0; j<i; j++)
            {
                lefti += (rating[j] < rating[i]);
                leftd += (rating[j] > rating[i]);
            }
            int righti = 0;
            int rightd = 0;
            for(int k = i+1; k<n; k++)
            {
                righti += (rating[i] < rating[k]);
                rightd += (rating[i] > rating[k]);
            }

            ans += lefti * righti + leftd*rightd;
       }
       return ans;
    }
};
16015