<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:
    def numTeams(self, rating: List[int]) -> int:
        return solve(rating)

def solve(nums):
    n = len(nums)
    ans = 0

    for i in range(n): # mid
        num = nums[i]
        leftSmaller = 0 # 左边 < nums[i] 的 数的个数
        rightLarger = 0 # 右边 > nums[i] 的 数的个数
        leftLarger = 0
        rightSmaller = 0

        for left in nums[:i]:
            if left < num: leftSmaller += 1
            elif left > num: leftLarger += 1
        for right in nums[i + 1:]:
            if num < right: rightLarger += 1
            elif right < num: rightSmaller += 1

        # 前提 数值 唯一，则 数的总数 刨去 小的 就剩 大的
        # leftLarger = i - leftSmaller
        # rightSmaller = n - 1 - i - rightLarger

        ans += leftSmaller * rightLarger
        ans += leftLarger * rightSmaller
    return ans
16500