Maximum Sum of Three Elements

You are given an array of n integers. Your task is to choose three distinct elements from the array such that their sum is maximized. Output the maximum sum and the 1-based indices of the chosen elements in ascending order.

Formally, let the array be \(a_1, a_2, \dots, a_n\). You need to find three distinct indices \(i, j, k\) such that

[ a_i + a_j + a_k = \max_{1 \leq i < j < k \leq n} (a_i + a_j + a_k), ]

and output the maximum sum on the first line, and the three indices (in ascending order) on the second line.

inputFormat

The first line contains a single integer n (\(n \ge 3\)), representing the number of elements in the array.

The second line contains n space-separated integers \(a_1, a_2, ..., a_n\), representing the elements of the array.

outputFormat

Output two lines:

• The first line should contain the maximum sum achievable by selecting three distinct elements.
• The second line should contain three 1-based indices of these elements in ascending order, separated by spaces.

## sample

5
1 2 3 4 5

12
3 4 5

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