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Maximum Sum Triplet


Problem Description

Given an array A containing N integers.

You need to find the maximum sum of triplet ( Ai + Aj + Ak ) such that 0 <= i < j < k < N and Ai < Aj < Ak.

If no such triplet exist return 0.



Problem Constraints

3 <= N <= 105.

1 <= A[i] <= 108.



Input Format

First argument is an integer array A.



Output Format

Return a single integer denoting the maximum sum of triplet as described in the question.



Example Input

Input 1:

 A = [2, 5, 3, 1, 4, 9]

Input 2:

 A = [1, 2, 3]



Example Output

Output 1:

 16

Output 2:

 6



Example Explanation

Explanation 1:

 All possible triplets are:-
    2 3 4 => sum = 9
    2 5 9 => sum = 16
    2 3 9 => sum = 14
    3 4 9 => sum = 16
    1 4 9 => sum = 14
  Maximum sum = 16

Explanation 2:

 All possible triplets are:-
    1 2 3 => sum = 6
 Maximum sum = 6



NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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