Given a list of N integers, the 3-sum problem is to determine whether there exists 3 integers in the list (not necessarily distinct) such that x + y + z = 0. Suppose that you are executing the brute force algorithm below on a computer that executes 1 billion operations (addition, increment, or comparison) per second. int brute

int brute(int a[], int N)

{

int i, j, k;

for (i = 0; i < N; i++)

for (j = 0; j < N; j++)

for (k = 0; k < N; k++)

if (a* + a[j] + a[k] == 0) return 1;
return 0; // none found
}
Estimate how many seconds it will take (in the worst case) to solve a problem of size N = 1,000?*