Given a binary tree, find height of it.

        1
     /     \
   10      39
  /
5
The above tree has a height of 3.
Note: Height of empty tree is considered 0.

Input Format:
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 denote 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 Format:
For each testcase, in a new line, print the height of tree.

Your Task:
You don't have to take input. Complete the function height() that takes node as parameter and returns the height. The printing is done by the driver code.

Constraints:
1 <= T <= 100
1 <= Number of nodes <= 105
1 <= Data of a node <= 105
Sum of N over all testcases doesn't exceed
 105

Example:
Input:

3
1 2 3
2 N 1 3 N
10 20 30 40 60 N N
Output:
2
3

3
Explanation:
Testcase1: The tree is
        1
     /      \
   2        3
So, the height would be 2.
Testcase2: The tree is
                           2
                              \
                               1 
                              /    
                          3
So, height would be 3.
Testcase3: The tree is

                           10
                        /        \
                     20         30
                  /       \
               40       60

So, height would be 3.

Note:The Input/Ouput format and Example given are used for system's internal purpose, and should be used by a user for Expected Output only. As it is a function problem, hence a user should not read any input from stdin/console. The task is to complete the function specified, and not to write the full code.

 

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

Contributor: Amit Khandelwal, Harshit Sidhwa
Author: kartik


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