Four Integers Summing to Zero

You are given four integer arrays $A$, $B$, $C$, and $D$, all of the same size.

Write a program that counts the number of tuples $(a, b, c, d)$ such that $A[a] + B[b] + C[c] + D[d] = 0$. Here $a$, $b$, $c$, and $d$ are indices from $0$ to $n-1$, choosing one element independently from each of the four arrays.

The first line contains the array size $n$ $(1 \le n \le 4000)$. Each of the next $n$ lines contains the integers belonging to $A$, $B$, $C$, and $D$, separated by spaces; the four integers on the $i$-th line are $A[i]$, $B[i]$, $C[i]$, and $D[i]$ in that order. The absolute value of every integer is at most $2^{28}$.

Print the number of tuples $(a, b, c, d)$ whose sum is $0$.