<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:
    map<int,set<int>> getSubSetSum(int lo, int hi, vector<int>& nums){
        int n = nums.size()/2;
        map<int,set<int>> res;
        for(int mask=0;mask<(1<<n);mask++){
            int cnt = 0,sum = 0;
            for(int i=lo;i<hi;i++){
                if( ( (1<<(i-lo)) & mask) > 0){
                    cnt++;
                    sum += nums[i];
                }
            }
            res[cnt].insert(sum);
        }

        return res;
    }
    bool possible(int szOfOneArray, int szOfSecondArray, int sum){
        if((sum*szOfSecondArray % (szOfOneArray+szOfSecondArray)) == 0){
            return true;
        }
        return false;
    }
    bool splitArraySameAverage(vector<int>& nums) {

        int n = nums.size();

        map<int,set<int>> subSetSumLowerHalf = getSubSetSum(0,n/2,nums);
        map<int,set<int>> subSetSumUpperHalf = getSubSetSum(n/2,n,nums);

        int sum = 0;
        for(auto el:nums){
            sum += el;
        }

        for(auto lowerHalf: subSetSumLowerHalf){
            for(auto upperHalf: subSetSumUpperHalf){
                int szOfOneArray = lowerHalf.first + upperHalf.first;
                int szOfSecondArray = n - szOfOneArray;
                if((szOfOneArray<=0 || szOfSecondArray<=0) || !possible(szOfOneArray, szOfSecondArray, sum)){
                    continue;
                }
                int firstHalfSum = sum - (sum*szOfSecondArray / n);
                cout<<szOfOneArray<<" "<<szOfSecondArray<<" "<<firstHalfSum<<" "<<sum-firstHalfSum<<endl;
                for(auto subsetSum: lowerHalf.second){
                    // if(subsetSum == firstHalfSum){
                    //     cout<<subsetSum<<endl;
                    //     return true;
                    // }
                    if(upperHalf.second.find(firstHalfSum - subsetSum) != upperHalf.second.end()){
                        cout<<subsetSum<<endl;
                        return true;
                    }
                }
            }
        }

        return false;
    }
};

// x = 5y/6

// 5*y + 6*y = sum*secondSize / total;
123073