<p>Given an integer array <code>nums</code>, return <em>the number of all the <strong>arithmetic subsequences</strong> of</em> <code>nums</code>.</p>

<p>A sequence of numbers is called arithmetic if it consists of <strong>at least three elements</strong> and if the difference between any two consecutive elements is the same.</p>

<ul>
	<li>For example, <code>[1, 3, 5, 7, 9]</code>, <code>[7, 7, 7, 7]</code>, and <code>[3, -1, -5, -9]</code> are arithmetic sequences.</li>
	<li>For example, <code>[1, 1, 2, 5, 7]</code> is not an arithmetic sequence.</li>
</ul>

<p>A <strong>subsequence</strong> of an array is a sequence that can be formed by removing some elements (possibly none) of the array.</p>

<ul>
	<li>For example, <code>[2,5,10]</code> is a subsequence of <code>[1,2,1,<strong><u>2</u></strong>,4,1,<u><strong>5</strong></u>,<u><strong>10</strong></u>]</code>.</li>
</ul>

<p>The test cases are generated so that the answer fits in <strong>32-bit</strong> integer.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [2,4,6,8,10]
<strong>Output:</strong> 7
<strong>Explanation:</strong> All arithmetic subsequence slices are:
[2,4,6]
[4,6,8]
[6,8,10]
[2,4,6,8]
[4,6,8,10]
[2,4,6,8,10]
[2,6,10]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [7,7,7,7,7]
<strong>Output:</strong> 16
<strong>Explanation:</strong> Any subsequence of this array is arithmetic.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1&nbsp; &lt;= nums.length &lt;= 1000</code></li>
	<li><code>-2<sup>31</sup> &lt;= nums[i] &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

class Solution {
    typedef long long ll;
    map<ll,vector<int>>adj;
    int dp[1001][2][1001];
    ll n;
    
    ll f(ll curr,ll picked,ll prev,vector<int>&nums){
        // if(curr >= n)return picked;

        ll diff = 1LL*nums[curr] - nums[prev];

        if(dp[curr][picked][prev] != -1)
            return dp[curr][picked][prev];

        ll ways = picked;

        ll next_val = nums[curr] + diff;

        if(adj[next_val].size() == 0)
            return ways;
        

        vector<int> &indices = adj[next_val];

        int ub = upper_bound(indices.begin(),indices.end(),curr) - indices.begin();

        for(int i = ub;i<indices.size();i++)
            ways += f(indices[i],1,curr,nums);
        

        return dp[curr][picked][prev] =  ways;
    }
public:
    int numberOfArithmeticSlices(vector<int>& nums) {
        n = nums.size();
        memset(dp, -1, sizeof(dp));

        for(int i = 0;i<n;i++)
            adj[nums[i]].push_back(i);

        ll ans = 0;
        for(int i = 0;i<n;i++){
            for(int j = i + 1;j<n;j++){
                ans += f(j,0,i,nums);
            }
        }
       
        return ans;
    }
};
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