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Maximum level sum


Problem Description

Given a Binary Tree denoted by root node A having integer value on nodes. You need to find maximum sum level in it.



Problem Constraints

1 <= number of nodes <= 105

1 <= value on nodes <= 105



Input Format

First and only argument is a root node of Binary Tree A.



Output Format

Return an integer denoting the maximum sum level in the tree.



Example Input

Input 1:

 Tree:      4
          /   \
         2     5
        / \   / \
       1  3  2   6

Input 2:

 Tree:      1
          /   \
         2     3
       /  \     \
      4    5     8
                / \
               6   7  



Example Output

Output 1:

 12

Output 2:

 17



Example Explanation

Explanation 1:

 Sum of all nodes of 0'th level is 4 
 Sum of all nodes of 1'th level is 7
 Sum of all nodes of 2'th level is 12
 Hence maximum sum is 12

Explanation 2:

 Sum of all nodes of 0'th level is 1
 Sum of all nodes of 1'th level is 5
 Sum of all nodes of 2'th level is 17
 Sum of all nodes of 3'th level is 13
 Hence maximum sum is 17



NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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