<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:
    int IncreasingOrderFunc(vector<int> &r,int in,int c,vector<vector<int>> &dpIncreasing)
    {
        if(c == 3) return 1;
        if(dpIncreasing[in][c] != -1) return dpIncreasing[in][c];

        int ans = 0;
        for(int i=in+1;i<r.size();i++)
        {
            
            if(r[in] > r[i]){
                ans += IncreasingOrderFunc(r,i,c+1,dpIncreasing);
            }
        }
        return dpIncreasing[in][c] = ans;
    }
    int DecreasingOrderFunc(vector<int> &r,int in,int c,vector<vector<int>> &dpDecreasing)
    {
        if(c == 3) return 1;

        if(dpDecreasing[in][c] != -1) return dpDecreasing[in][c];

        int ans  = 0;
        for(int i=in+1;i<r.size();i++)
        {
            if(r[in] < r[i]){
                ans += DecreasingOrderFunc(r,i,c+1,dpDecreasing);
            }

        }

        return dpDecreasing[in][c] = ans;
    }
    int numTeams(vector<int>& r) {

        int ans = 0;

        vector<vector<int>> dpIncreasing((1000),vector<int> (3,-1));
        vector<vector<int>> dpDecreasing((1000),vector<int> (3,-1));

        for(int i=0;i<r.size();i++)
        {
            ans += IncreasingOrderFunc(r,i,1,dpIncreasing);
            ans += DecreasingOrderFunc(r,i,1,dpDecreasing);
        }

        return ans;
    }
};
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