Given a Binary Tree, find the maximum width of it.  Maximum width is maximum number of nodes in any level.  For example, maximum width of following tree is 4 as there are 4 nodes at 3rd level

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

Input:
The task is to complete the method that takes root of tree as an argument.

There are multiple test cases. For each test case, this method will be called individually.

Output:
The function should return maximum width of tree.

Constraints:
1 <=T<= 30
1 <= Size of arrays <= 100
1 <= Values in arrays <= 1000

Example:
Input:
2
2
1 2 R 1 3 L
4
10 20 L 10 30 R 20 40 L 20 60 R
 

Output:
2
2

There are two test casess.  First case represents a tree with 3 nodes, 2 edges. Here root is 1, left child of 1 is 3 and right child of 1 is 2.   Second test case represents a tree with 4 edges and 5 nodes.

Note:The Input/Ouput format and Example given above 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, and should not print anything on stdout/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 **