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Write a Python function `sum_of_subarray_products` that computes the sum of the products of all possible subarrays of a given list of integers. A subarray is a contiguous portion of the array. For example, for the array `[1, 2, 3]`, the subarrays are `[1]`, `[2]`, `[3]`, `[1, 2]`, `[2, 3]`, and `[1, 2, 3]`. #### Example Usage: ```python [main.nopy] print(sum_of_subarray_products([1, 2, 3])) # Output: 20 print(sum_of_subarray_products([1, 2])) # Output: 5 print(sum_of_subarray_products([1, 2, 3, 4])) # Output: 84 ``` #### Constraints: - The input list will contain at least one integer. - The integers in the list will be non-negative. Implement the function efficiently.
def sum_of_subarray_products(arr):
"""
Calculate the sum of the products of all possible subarrays of the given list.
Args:
arr (list): A list of integers.
Returns:
int: The sum of the products of all possible subarrays.
"""
# Placeholder for the solution
pass