Given a binary tree with a value associated with each node, we need to choose a subset of these nodes such that sum of chosen nodes is maximum under a constraint that no two chosen node in subset should be directly connected that is, if we have taken a node in our sum then we can’t take its any children in consideration and vice versa.

                                               

Input:
First line of input contains the number of test cases T. For each test case, there will be only a single line of input which is a string representing the tree as described below: 

  1. The values in the string are in the order of level order traversal of the tree where, numbers denotes node values, and a character “N” denotes NULL child.

  2. For example:

For the above tree, the string will be: 1 2 3 N N 4 6 N 5 N N 7 N

Output:
For each test case prints the maximum sum such that no two nodes are adjacent.

Constraints:
1 <= T <= 100
1 <= N <= 1000

Your Task:
This is a functional problem. User need to complete function getMaxSum() which accepts root node of the tree as parameter and returns the maximum sum .

Example:
Input:

2
11 1 2
1 2 3 4 N 5 6
Output:
11
16

Explanation:
Testcase 1: 
The maximum sum is sum of node 11.
Testcase 2: The maximum sum is sum of nodes 1 4 5 6 , i.e 16. These nodes are non adjacent.

** For More Input/Output Examples Use 'Expected Output' option **

Author: SIDG


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