<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 Tree {
    Tree *left = nullptr, *right = nullptr;
    int val = 0, cnt_left = 0;
    Tree(int val) : val(val) {}
};
int count(Tree* root, int val) {
    if (root == nullptr)
        return 0;
    if (val < root->val)
        return count(root->left, val);
    return 1 + root->cnt_left + count(root->right, val);
}
Tree* insert(Tree* root, int val) {
    if (root == nullptr)
        return new Tree(val);
    if (val < root->val) {
        ++root->cnt_left;
        root->left = insert(root->left, val);
    }
    else
        root->right = insert(root->right, val);
    return root;
}
Tree* remove(Tree* root, int val) {
    if (root == nullptr)
        return nullptr;
    if (root->val == val) {
        if (root->left == nullptr)
            return root->right;
        auto rightmost = root->left;
        while (rightmost->right != nullptr)
            rightmost = rightmost->right;
        rightmost->right = root->right;
        return root->left;
    }
    if (val < root->val) {
        --root->cnt_left;
        root->left = remove(root->left, val);
    }
    else
        root->right = remove(root->right, val);
    return root;
}
class Solution {
public:
int numTeams(vector<int>& rating) {
    Tree left(rating.front()), right(rating.back());
    int res = 0, sz = rating.size();
    for (auto i = 1; i < sz - 1; ++i)
        insert(&right, rating[i]);
    for (auto i = 1; i < sz - 1; ++i) {
        remove(&right, rating[i]);
        int l_sm = count(&left, rating[i]), l_lg = i - l_sm;
        int r_sm = count(&right, rating[i]), r_lg = (sz - 1 - i - r_sm) ;
        res += l_sm * r_lg + l_lg * r_sm;
        insert(&left, rating[i]);
    }
    return res;
}
};
19040