You are given a nested list of integers nestedList. Each element is either an integer or a list whose elements may also be integers or other lists.

The depth of an integer is the number of lists that it is inside of. For example, the nested list [1,[2,2],[[3],2],1] has each integer's value set to its depth.

Return the sum of each integer in nestedList multiplied by its depth.

 

Example 1:

Input: nestedList = [[1,1],2,[1,1]]
Output: 10
Explanation: Four 1's at depth 2, one 2 at depth 1. 1*2 + 1*2 + 2*1 + 1*2 + 1*2 = 10.

Example 2:

Input: nestedList = [1,[4,[6]]]
Output: 27
Explanation: One 1 at depth 1, one 4 at depth 2, and one 6 at depth 3. 1*1 + 4*2 + 6*3 = 27.

Example 3:

Input: nestedList = [0]
Output: 0

 

Constraints:

• 1 <= nestedList.length <= 50
• The values of the integers in the nested list is in the range [-100, 100].
• The maximum depth of any integer is less than or equal to 50.