If the depth of a tree is smaller than 5, then this tree can be represented by an array of three-digit integers. For each integer in this array:

• The hundreds digit represents the depth d of this node where 1 <= d <= 4.
• The tens digit represents the position p of this node in the level it belongs to where 1 <= p <= 8. The position is the same as that in a full binary tree.
• The units digit represents the value v of this node where 0 <= v <= 9.

Given an array of ascending three-digit integers nums representing a binary tree with a depth smaller than 5, return the sum of all paths from the root towards the leaves.

It is guaranteed that the given array represents a valid connected binary tree.

 

Example 1:

Input: nums = [113,215,221]
Output: 12
Explanation: The tree that the list represents is shown.
The path sum is (3 + 5) + (3 + 1) = 12.

Example 2:

Input: nums = [113,221]
Output: 4
Explanation: The tree that the list represents is shown. 
The path sum is (3 + 1) = 4.

 

Constraints:

• 1 <= nums.length <= 15
• 110 <= nums[i] <= 489
• nums represents a valid binary tree with depth less than 5.