Sum of Absolute Differences

ArrayMathPrefix Sum

Given an array of integers, compute the sum of absolute differences between each element and every other element in the array. The absolute difference between two integers a and b is given by |a - b|, where |x| denotes the absolute value of x.

Example 1

Input

[
  1,
  2,
  3
]

Output

Explanation. The absolute differences are |1-2|=1, |1-3|=2, and |2-3|=1. So the sum is 1+2+1+1+2+1=6.

Example 2

Input

[
  10,
  12
]

Output

Explanation. Since there are only two elements, the sum of the absolute differences is |10-12|=2.

Example 3

Input

[
  5,
  -3,
  6
]

Output

Explanation. Calculating each pair's absolute difference results in |5+3|=8, |5-6|=1, |-3-6|=9. Sum for all pairs is 8+1+9+8+1+1=28.

Follow-up: Can you solve this problem in an optimized way to reduce computational redundancy?

Constraints:

The input array will have at least two integers and at most 100 integers, each within the range -1000 to 1000.

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