<p>You are given an integer array <code>nums</code>.</p>

<p>You should move each element of <code>nums</code> into one of the two arrays <code>A</code> and <code>B</code> such that <code>A</code> and <code>B</code> are non-empty, and <code>average(A) == average(B)</code>.</p>

<p>Return <code>true</code> if it is possible to achieve that and <code>false</code> otherwise.</p>

<p><strong>Note</strong> that for an array <code>arr</code>, <code>average(arr)</code> is the sum of all the elements of <code>arr</code> over the length of <code>arr</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [1,2,3,4,5,6,7,8]
<strong>Output:</strong> true
<strong>Explanation:</strong> We can split the array into [1,4,5,8] and [2,3,6,7], and both of them have an average of 4.5.
</pre>

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

<pre>
<strong>Input:</strong> nums = [3,1]
<strong>Output:</strong> false
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 30</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    bool splitArraySameAverage(vector<int>& nums) {
        int n = nums.size()/2, sum = 0;
        if(nums.size() <= 1)return false;
        for(auto x:nums)sum += x;
        unordered_map<int,set<int>>mp1,mp2;
        for(int i=1;i<(1<<n);i+=1){
            int sz = 0;
            int sumi = 0;
            int j=n-1;
            int bits = i;
            while(bits){
               if(bits&1){
                sumi+=nums[j];
                sz+=1;
               }
               j-=1;
               bits>>=1;
            }
            if(nums.size()*sumi == sz*sum)return true;
            mp1[sz].insert(sumi);
        }
        for(int i=1;i<(1<<(nums.size()-n));i+=1){
            int sz = 0;
            int sumi = 0;
            int j=nums.size()-1;
            int bits = i;
            while(bits){
               if(bits&1){
                sumi+=nums[j];
                sz+=1;
               }
               j-=1;
               bits>>=1;
            }
            if(nums.size()*sumi == sz*sum)return true;
            mp2[sz].insert(sumi);
        }
        for(auto x:mp1){
            for(auto y:mp2){
                int n1 = x.first+y.first;
                if(n1 == nums.size() || ((sum*n1)%nums.size()))continue;
                int sum1 = (sum*n1)/nums.size();
                for(auto z:x.second){
                    if(y.second.find(sum1-z) != y.second.end())return true;
                }
            }
        }
        return false;
    }
};
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