Given a nested list of integers, where each element is either an integer or a list, compute the sum of all integers in the list weighted by their depth. The depth of the top-level elements is 1. For example, an integer at depth 3 contributes its value multiplied by 3 to the sum. Implement a function that takes a nested list and returns the weighted sum.
Example 1
Input: [[2], 3, [4, [5]]]
Output: 2*2 + 3*1 + 4*2 + 5*3 = 4 + 3 + 8 + 15 = 30
Explanation: 2 at depth 2, 3 at depth 1, 4 at depth 2, 5 at depth 3
Example 2
Input: [1, [2, [3, [4]]]]
Output: 1*1 + 2*2 + 3*3 + 4*4 = 1 + 4 + 9 + 16 = 30
Explanation: 1 at depth 1, 2 at depth 2, 3 at depth 3, 4 at depth 4
Constraints
Case 1
Input: [5, [6, [7]]]
Expected: 5*1 + 6*2 + 7*3 = 5 + 12 + 21 = 38
Case 2
Input: [[[1]], 2]
Expected: 1*3 + 2*1 = 3 + 2 = 5
Case 3
Input: [[-1, [-2]], 3]
Expected: -1*1 + -2*2 + 3*1 = -1 + -4 + 3 = -2
Case 4
Input: [[], 10]
Expected: 10*1 = 10
Case 5
Input: [[[0]]]
Expected: 0*3 = 0