A non-empty zero-indexed array A of N integers is given. A pair of integers (P, Q), such that 0 ≤ P ≤ Q < N, is called a slice of array A. Thesum of a slice (P, Q) is the total of A[P] + A[P+1] + ... + A[Q].

A min abs slice is a slice whose absolute sum is minimal.

For example, array A such that:

  A[0] = 2
  A[1] = -4
  A[2] = 6
  A[3] = -3
  A[4] = 9

contains the following slices, among others:

• (0, 1), whose absolute sum = |2 + (−4)| = 2
• (0, 2), whose absolute sum = |2 + (−4) + 6| = 4
• (0, 3), whose absolute sum = |2 + (−4) + 6 + (−3)| = 1
• (1, 3), whose absolute sum = |(−4) + 6 + (−3)| = 1
• (1, 4), whose absolute sum = |(−4) + 6 + (−3) + 9| = 8
• (4, 4), whose absolute sum = |9| = 9

Both slices (0, 3) and (1, 3) are min abs slices and their absolute sum equals 1.

Write a function:

int solution(int A[], int N);

that, given a non-empty zero-indexed array A consisting of N integers, returns the absolute sum of min abs slice.

For example, given:

  A[0] = 2
  A[1] = -4
  A[2] = 6
  A[3] = -3
  A[4] = 9

the function should return 1, as explained above.

Assume that:

• N is an integer within the range [1..100,000];
• each element of array A is an integer within the range [−10,000..10,000].

Complexity:

• expected worst-case time complexity is O(N*log(N));
• expected worst-case space complexity is O(N), beyond input storage (not counting the storage required for input arguments).

Elements of input arrays can be modified.