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ambitious

Find the maximum sum of a compact subsequence of array elements after performing a single swap operation.

Programming language:

A non-empty array A consisting of N integers is given. A pair of integers (P, Q), such that 0 ≤ P ≤ Q < N, is called a *slice* of array A. The *sum* of a slice (P, Q) is the total of A[P] + A[P+1] + ... + A[Q]. The *maximum sum* is the maximum sum of any slice of A.

For example, consider array A such that:

For example (0, 1) is a slice of A that has sum A[0] + A[1] = 5. This is the maximum sum of A.

You can perform a single swap operation in array A. This operation takes two indices I and J, such that 0 ≤ I ≤ J < N, and exchanges the values of A[I] and A[J]. The goal is to find the maximum sum you can achieve after performing a single swap.

For example, after swapping elements 2 and 4, you will get the following array A:

After that, (0, 3) is a slice of A that has the sum A[0] + A[1] + A[2] + A[3] = 9. This is the maximum possible sum of A after a single swap.

Write a function:

class Solution { public int solution(int[] A); }

that, given a non-empty array A of N integers, returns the maximum possible sum of any slice of A after a single swap operation.

For example, given:

the function should return 9, as explained above.

Write an ** efficient** algorithm for the following assumptions:

- 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].

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