<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:
    
    
    void update(vector<int>&tree,int index,int s,int e,int id){
        if(s>e)return; 
        if(id<s || id>e)return;
        if(s==e){
            tree[index]=1;
            return;
        }
        int mid=(s+e)/2;
        update(tree,2*index,s,mid,id);
        update(tree,2*index+1,mid+1,e,id);
        tree[index]=tree[2*index]+tree[2*index+1];
        return; 
    }
    int query(vector<int>&tree,int index,int s,int e,int qs,int qe){
        if(s>e)return 0; 
        if(s>qe || e<qs)return 0; 
        if(s>=qs && e<=qe){
            return tree[index];
        }
        int mid=(s+e)/2;
        int l=query(tree,2*index,s,mid,qs,qe);
        int r=query(tree,2*index+1,mid+1,e,qs,qe);
        return l+r; 
    }
    
    
    // CC + ST
    int numTeams(vector<int>& rating) {
        int n=rating.size();
        
        vector<int> ash;
        for(auto&x:rating){
            ash.push_back(x);
        }
        sort(ash.begin(),ash.end());
        unordered_map<int,int> mp;
        for(int i=0;i<n;++i){
            mp[ash[i]]=i;
        }
        vector<int> tree(4*n+1);
        vector<pair<int,int>> ll(n);
        vector<pair<int,int>> rr(n);
        
        for(int i=0;i<n;++i){
            int ff=query(tree,1,0,n-1,0,mp[rating[i]]-1);
            int ss=query(tree,1,0,n-1,mp[rating[i]]+1,n-1);
            ll[i]={ff,ss};
            //cout<<ff<<" "<<ss<<"\n";
            update(tree,1,0,n-1,mp[rating[i]]);
        }
        for(auto&x:tree)x=0;
        for(int i=n-1;i>=0;--i){
            int ff=query(tree,1,0,n-1,0,mp[rating[i]]-1);
            int ss=query(tree,1,0,n-1,mp[rating[i]]+1,n-1);
            rr[i]={ff,ss};
            update(tree,1,0,n-1,mp[rating[i]]);
        }
        int ans=0;
        for(int i=0;i<n;++i){
            ans+=(ll[i].first*rr[i].second);
            ans+=(ll[i].second*rr[i].first);
        }
        return ans;
        
        
        
        
    }
};
15259