Given a Binary Tree (BT), convert it to a Doubly Linked List(DLL) In-Place. The left and right pointers in nodes are to be used as previous and next pointers respectively in converted DLL. The order of nodes in DLL must be same as Inorder of the given Binary Tree. The first node of Inorder traversal (leftmost node in BT) must be the head node of the DLL.


The 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

For each test case, in a new line, print front to end and back to end traversals of DLL.

Your Task:
You don't have to take input. Complete the function bToDLL() that takes node and head as a parameter. The driver code prints the DLL both ways.

Expected Time Complexity: O(N).
Expected Auxiliary Space: O(H).
Note: H is the height of the tree and this space is used implicitly for recursion stack.

1 <= T <= 100
1 <= Number of nodes <= 1000
1 <= Data of a node <= 1000


1 3 2
10 20 30 40 60

3 1 2
2 1 3
40 20 60 10 30
30 10 60 20 40

Testcase1: The tree is
     /      \
   3       2
So, DLL would be 3<=>1<=>2
Testcase2: The tree is
                        /        \
                     20         30
                  /       \
               40       60
So, DLL would be 40<=>20<=>60<=>10<=>30.


Note: The Input/Output format and Examples given are used for the 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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