Sum of All Subarrays

Problem Description

You are given an integer array A of length N. You have to find the sum of all subarray sums of A. More formally, a subarray is defined as a contiguous part of an array which we can obtain by deleting zero or more elements from either end of the array. A subarray sum denotes the sum of all the elements of that subarray.

Note : Be careful of integer overflow issues while calculations. Use appropriate datatypes.

Problem Constraints

1 <= N <= 10^5
1 <= Ai <= 10^4

Input Format

The first argument is the integer array A.

Output Format

Return a single integer denoting the sum of all subarray sums of the given array.

Example Input

Input 1:
A = [1, 2, 3]

Input 2:
A = [2, 1, 3]

Example Output

Output 1:
20

Output 2:
19

Example Explanation

Explanation 1:
The different subarrays for the given array are: [1], [2], [3], [1, 2], [2, 3], [1, 2, 3].
Their sums are: 1 + 2 + 3 + 3 + 5 + 6 = 20

Explanation 2:
The different subarrays for the given array are: [2], [1], [3], [2, 1], [1, 3], [2, 1, 3].
Their sums are: 2 + 1 + 3 + 3 + 4 + 6 = 19

Output