<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 BIT {
public:
    int n;
    vector<int>bit;

    BIT(int n){
        this->n = n;
        bit.resize(n+1, 0);
    }

    void update(int i, int x){
        i++;
        for(;i<=n;i+=(i&(-i))){
            bit[i] += x;
        }
    }

    int query(int i){
        i++;
        int sum = 0;
        for(;i>0;i-=(i&(-i))){
            sum += bit[i];
        }

        return sum;
    }

};



class Solution {
public:

    int numTeams(vector<int>& rating) {
        int n = rating.size();
        BIT* tree = new BIT(n + 5);
        BIT* tree1 = new BIT(n + 5);
        unordered_map<int,int>m;
        set<int>s;
        int curr = 1;
        for(int i=0;i<n;i++){
            s.insert(rating[i]);
        }
        for(auto it:s){
            m[it] = curr;
            curr++;
        }
        vector<int>v, v1;
        int ans = 0;
        for(int i=0;i<n;i++){
            int val = tree->query(m[rating[i]] - 1);
            v.push_back(val);
            v1.push_back(i-val);
            tree->update(m[rating[i]], 1);
        }
        int r = m.size();

        for(int i=n-1;i>=0;i--){
            int val = tree1->query(m[rating[i]]-1);
            ans += ((n-i-1-val) * v[i]) + (val * v1[i]);
            tree1->update(m[rating[i]], 1);
        }
        return ans;
    



    }
};
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