<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): n(n), BIT(n){}

    void add(int idx, int x){
        for (; idx<n; idx=idx|(idx+1))
            BIT[idx] += x;
    }

    int sum(int idx){
        int ans = 0;
        for (; idx>= 0; idx=(idx&(idx+1))-1)
            ans+=BIT[idx];
        return ans;
    }

    int sum(int l, int r){
        return sum(r)-sum(l-1);
    }
};

class Solution {
public:
    static int  numTeams(vector<int>& rating) {
        const int n=rating.size();
        const int m=*max_element(rating.begin(), rating.end());

        FenwickTree L(m+1), R(m+1);

        for(int x: rating) R.add(x, 1);

        int cnt=0;
        for(int x: rating){
            R.add(x, -1);

            int LLess=L.sum(x-1);
            int RLess=R.sum(x-1);
            int LBigger=L.sum(x+1, m);
            int RBigger=R.sum(x+1, m);

            cnt+=LLess*RBigger+LBigger*RLess;

            L.add(x, 1);
        }
        return cnt;
    }
};




auto init = []() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    return 'c';
}();
21460