Given n distinct integers, we want to know how many triples (x, y, z), where x y z, sum to exactly zero. Note that the order of the triple does not matter, i.e., (x, y, z) is considered to be the same as (z, y, x).Example: There are 4 triples that sum to zero in the array:

[3 4 2 1 4 0 1]

i.e., the triples (3, 4, 1), (3, 2, 1), (4, 4, 0), (1, 0, 1).

Consider the following pseudocode, which, given an input of n distinct integers, counts the number of triples that sum exactly to zero:

3-Sum-to-0(A[1n]) 01 count = 0 02 for i = 1 to n 03 for j = i + 1 to n 04 for k = j + 1 to n 05 if A[i] + A[j] + A[k] == 0 06 count = count + 1 07 return count

1. Let T(n) be the number of times the array A is accessed (for values A[i], A[j],A[k]) as a function of input size n. Express T(n) as a summation (actually three nested summations). Find T(n), i.e., simplify the summation. Show all your work.