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# MAXSPPROD

Problem Description

You are given an array A containing N integers. The special product of each ith integer in this array is defined as the product of the following:

1. LeftSpecialValue: For an index i, it is defined as the index j such that A[j]>A[i] and (i>j). If multiple A[j]'s are present in multiple positions, the LeftSpecialValue is the maximum value of j. Here LeftSpecialValue is the index j and not A[j].
2. RightSpecialValue: For an index i, it is defined as the index j such that A[j]>A[i] and (j>i). If multiple A[j]'s are present in multiple positions, the RightSpecialValue is the minimum value of j. Here RightSpecialValue is the index j and not A[j].

Write a program to find the maximum special product of any integer in the array. In other words you have to find the maximum for all i (0<i<n-1) of product of l and r such that l is the LeftSpecialValue and r is the RightSpecialValue of an index i.

Note that the array A is zero indexed.

Problem Constraints

1 <= N <= 105
1 <= A[i] <= 109

Input Format

First and only argument is an integer array A.

Output Format

Return an integer denoting the maximum special product of any integer.

Example Input

Input 1:

` A = [1, 4, 3, 4]`

Input 2:

` A = [10, 7, 100]`

Example Output

Output 1:

` 3`

Output 2:

` 0`

Example Explanation

Explanation 1:

``` For A[2] = 3, LeftSpecialValue is 1 and RightSpecialValue is 3.
So, the ans is 1*3 = 3.
```

Explanation 2:

` There is not any integer having maximum special product > 0. So, the ans is 0.`

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 question? Checkout Sample Codes for more details.
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