Given a nested list of integers, return the sum of all integers in the list weighted by their depth.

Each element is either an integer, or a list -- whose elements may also be integers or other lists.

Example 1:
Given the list[[1,1],2,[1,1]], return10. (four 1's at depth 2, one 2 at depth 1)

Example 2:
Given the list[1,[4,[6]]], return27. (one 1 at depth 1, one 4 at depth 2, and one 6 at depth 3; 1 + 4*2 + 6*3 = 27)

/**
 * // This is the interface that allows for creating nested lists.
 * // You should not implement it, or speculate about its implementation
 * public interface NestedInteger {
 *     // Constructor initializes an empty nested list.
 *     public NestedInteger();
 *
 *     // Constructor initializes a single integer.
 *     public NestedInteger(int value);
 *
 *     // @return true if this NestedInteger holds a single integer, rather than a nested list.
 *     public boolean isInteger();
 *
 *     // @return the single integer that this NestedInteger holds, if it holds a single integer
 *     // Return null if this NestedInteger holds a nested list
 *     public Integer getInteger();
 *
 *     // Set this NestedInteger to hold a single integer.
 *     public void setInteger(int value);
 *
 *     // Set this NestedInteger to hold a nested list and adds a nested integer to it.
 *     public void add(NestedInteger ni);
 *
 *     // @return the nested list that this NestedInteger holds, if it holds a nested list
 *     // Return null if this NestedInteger holds a single integer
 *     public List<NestedInteger> getList();
 * }
 */
class Solution {
    public int depthSum(List<NestedInteger> nestedList) {
        if (nestedList == null || nestedList.size() == 0) return 0;

        return helper(nestedList, 1);
    }

    private int helper(List<NestedInteger> inList, int level){
        int ans = 0;

        for (NestedInteger ni : inList){
            if (ni.isInteger()){
                ans += level * ni.getInteger();        
            }
            else{
                ans += helper(ni.getList(), level + 1);
            }

            //System.out.println("level: " + level + " ans: " + ans);
        }

        return ans;
    }
}