Rewriting the Sum of indexes i and j across the ordered real numbers x(1), x(1) ... x(n) with a modulus consideration

Question

Question is in image (sorry I don't know how to do the type set)

My attempt is halfway here and I got stuck.

Given LHS

= Sum (i=1 to i=n) for { Sum (j=1 to j=n) [x(i) - x(n)] where [u] denotes modulus of u }

= Sum (i=1 to i=n) for [x(i) - x(1)] + [x(i) - x(2)] + ... + [x(i) - x(n)]

= Sum (i=1 to i=n) for (x(i) - x(1)) + (x(i) - x(2)) + (x(i) - x(i-1)) + (x(i) - x(i))

• ... + (x(i+1) - x(i)) + (x(i+2) - x(i)) + ... + (x(n) - x(i))

= Sum (i=1 to i=n) for ( { (2i - n - 1) } x(i) - x(1) - x(2) - ... - x(i) + x(i+1) +x(i+2) +... + x(n) )

I am stuck here.

Any help is appreciated, thank you