<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:

//int dp[32][31][300001];
bool f(int i,int n1,int size,int sum,vector<int>&nums,vector<vector<vector<bool>>>&dp){
    int n=nums.size();
    if(size>n1){
        return false;
    }
    if(size==n1){
        return sum==0;
    }
    if(sum<0){
        return false;
    }
    if(i==n){
        return false;
    }
    if(dp[i][size][sum]==false){
        return dp[i][size][sum];
    }
    bool ans=false;
    ans=ans|(f(i+1,n1,size+1,sum-nums[i],nums,dp));
    ans=ans|(f(i+1,n1,size,sum,nums,dp));
    return dp[i][size][sum]=ans;
}
    bool splitArraySameAverage(vector<int>& nums) {
     int n=nums.size();
     int totsum=0;
     for(int i=0;i<n;i++){
        totsum=totsum+nums[i];
     }  
    
     vector<vector<vector<bool>>>dp(n+1,vector<vector<bool>>(n+1,vector<bool>(totsum+1,true)));
     for(int i=1;i<=n-1;i++){
        if((totsum*i)%n==0){
            if(f(0,i,0,(totsum*i)/n,nums,dp)){
                return true;
            }
        }
     }
     return false;
    }
};
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