title: Sum of 4 integers in 4 arrays
body: <p>Given four lists A, B, C, D of integer values, compute how many tuples (i, j, k, l) there are such that A[i] + B[j] + C[k] + D[l] is zero.</p>
  
  <p>To make problem a bit easier, all A, B, C, D have same length of N where 0 ≤ N ≤ 500. All integers are in the range of -228 to 228 - 1 and the result is guaranteed to be at most 231 - 1.</p>
  
  <p>Example:</p>
  
  <pre><code>Input:
  A = [ 1, 2]
  B = [-2,-1]
  C = [-1, 2]
  D = [ 0, 2]
  </code></pre>
  
  <p>Output:
  2</p>
  
  <p>Explanation:
  The two tuples are:</p>
  
  <pre><code>1. (0, 0, 0, 1) -&gt; A[0] + B[0] + C[0] + D[1] = 1 + (-2) + (-1) + 2 = 0
  2. (1, 1, 0, 0) -&gt; A[1] + B[1] + C[0] + D[0] = 2 + (-1) + (-1) + 0 = 0
  </code></pre>
  
  <p>I just came up with a solution that concatenates all the vectors and find the 4 sum. But I know there is a better solution. Would someone explain a better solution ? I just see codes using O(N^2) but I can't understand it.</p>