Maximum Sublist Sum

You are given a list of integers. Your task is to find a contiguous subarray (sublist) that yields the maximum possible sum. In addition, you must output the start and end indices (1-based) of this subarray. If multiple subarrays yield the same maximum sum, choose the one with the smallest start index.

If the input list is empty, the output should be 0 0 0.

The mathematical formulation of the problem is to find indices \(i\) and \(j\) (with \(1 \le i \le j \le n\)) such that \[ S = \sum_{k=i}^{j} a_k \] is maximized.

This problem can be efficiently solved using Kadane's algorithm.

inputFormat

The first line of input contains an integer \(n\) indicating the number of elements in the list. If \(n > 0\), the second line contains \(n\) space-separated integers representing the list.

If \(n = 0\), there will be no second line.

outputFormat

Output three space-separated integers: the maximum sublist sum, the 1-based start index, and the 1-based end index of the sublist that produces this sum.

If the list is empty, output 0 0 0.

## sample

9
-2 1 -3 4 -1 2 1 -5 4

6 4 7

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