<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 su(int i,vector<int>&rating,int prev,int n,vector<vector<vector<int>>>&dp,int k){
    if(i>=rating.size()){
        if(n==3){
            return dp[prev+1][n][k]=1;
        }
        return dp[prev+1][n][k]=0;
    }
    if(n==3){
        return dp[prev+1][n][k]=1;
    }
    if(dp[prev+1][n][k]!=-1){
    //    cout<<i<<" "<<n<<"->"<<dp[prev+1][n]<<endl;
        return dp[prev+1][n][k];
    }
    if(prev==-1){
        return dp[prev+1][n][k]=su(i+1,rating,i,n+1,dp,0)+su(i+1,rating,i,n+1,dp,1)+su(i+1,rating,prev,n,dp,k);
    }else if(rating[i]>rating[prev] && k==0){
        return dp[prev+1][n][k]=su(i+1,rating,i,n+1,dp,k)+su(i+1,rating,prev,n,dp,k);
    }else if(rating[i]<rating[prev] && k==1){
         return dp[prev+1][n][k]=su(i+1,rating,i,n+1,dp,k)+su(i+1,rating,prev,n,dp,k);
    }else{
        return dp[prev+1][n][k]=su(i+1,rating,prev,n,dp,k);
    }
}

    int numTeams(vector<int>& rating) {
       // vector<vector<int>>dp(rating.size()+5,vector<int>(rating.size()+5,-1));
        vector<vector<vector<int>>>dp(rating.size()+5,vector<vector<int>>(5,vector<int>(2,-1)));
        //+su2(0,rating,100007,0,dp1)
        return su(0,rating,-1,0,dp,0);
    }
};
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