<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:
    int findDescending(int i, int count, vector<int>& rating) {
        if (count == 0) return 1;
        int ret = 0;
        for (int j = i+1; j < rating.size(); ++j) {
            if (rating[i] > rating[j]) ret += findDescending(j,count-1,rating);
        }
        return ret;
    }
    int findAscending(int i, int count, vector<int>& rating) {
        if (count == 0) return 1;
        int ret = 0;
        for (int j = i+1; j < rating.size(); ++j) {
            if (rating[i] < rating[j]) ret += findAscending(j,count-1,rating);
        }
        return ret;
    }
    int numTeams(vector<int>& rating) {
        int res = 0;
        vector<vector<int>> dp1(rating.size(),vector<int>(3,0));
        for (int i = 0; i < dp1.size(); ++i) dp1[i][0] = 1;
        vector<vector<int>> dp2 = dp1;
        for (int i = rating.size()-1; i >= 0; --i) {
            for (int count = 1; count <= 2; ++count) {
                int ret1 = 0;
                int ret2 = 0;
                for (int j = i+1; j < rating.size(); ++j) {
                    if (rating[i] < rating[j]) ret1 += dp1[j][count-1];
                    if (rating[i] > rating[j]) ret2 += dp2[j][count-1];
                }
                dp1[i][count] = ret1;
                dp2[i][count] = ret2;
                // cout << i << " " << count << " " << dp1[i][count] << endl;
            }
            res += dp1[i][2] + dp2[i][2];
        }
        return res;

        // int ret = 0;
        // for (int i = 0; i < rating.size()-2; ++i) {
        //     ret += findAscending(i,2,rating) + findDescending(i,2,rating);
        // }
        // return ret;
    }
};
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