<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>

struct FenwickTree{
    vector<int> bit;
    int n;
    FenwickTree(int n){
        this->n=n;
        bit.assign(n,0);
    }
    int sum(int r){
        int ret=0;
        for(;r>=0;r=(r&(r+1))-1)ret+=bit[r];
        return ret;
    }
    void add(int idx){
        for(;idx<n;idx|=(idx+1))bit[idx]++;
    }
};


class Solution {
public:
    int numTeams(vector<int>& rating) {
        int maxi=*max_element(rating.begin(),rating.end());
        FenwickTree left(maxi+2),right(maxi+2);
        vector<int>smoll(rating.size(),0),smolr(rating.size(),0);
        for(int i=0;i<rating.size();i++){
            left.add(rating[i]);
            right.add(rating[rating.size()-i-1]);
            smoll[i]=left.sum(rating[i])-1;
            smolr[rating.size()-i-1]=right.sum(rating[rating.size()-i-1])-1;
        }
        int ans=0;
        for(int i=0;i<rating.size();i++){
            ans+=(i-smoll[i])*smolr[i];
            ans+=(rating.size()-smolr[i]-1-i)*smoll[i];
        }
        return ans;
    }
};
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