Given a binary tree, print the bottom view from left to right.
A node is included in bottom view if it can be seen when we look at the tree from bottom.

                      20
                    /    \
                  8       22
                /   \        \
              5      3       25
                    /   \      
                  10    14

For the above tree, the bottom view is 5 10 3 14 25.
If there are multiple bottom-most nodes for a horizontal distance from root, then print the later one in level traversal. For example, in the below diagram, 3 and 4 are both the bottommost nodes at horizontal distance 0, we need to print 4.

                      20
                    /    \
                  8       22
                /   \     /   \
              5      3 4     25
                     /    \      
                 10       14

For the above tree the output should be 5 10 4 14 25.

Input Format:

First line of input contains the number of test cases T. For each test case, there will be two lines: 

  1. First line of each test case will be an integer N denoting the number of parent child relationships.
  2. Second line of each test case will print the level order traversal of the tree in the form of N space-separated triplets. The description of triplets is as follows:
    • ​​Each triplet will contain three space-separated elements of the form (int, int, char).
    • The first integer element will be the value of parent. 
    • The second integer will be the value of corresponding left or right child. In case the child is null, this value will be -1.
    • The third element of triplet which is a character can take any of the three values ‘L’, ‘R’ or ‘N’. L denotes that the children is a left child, R denotes that the children is a Right Child and N denotes that the child is NULL.

Please note that the relationships are printed only for internal nodes and not for leaf nodes.  

Output Format:
The function should print nodes in the bottom view of Binary Tree. Your code should not print a newline, it is added by the caller code that runs your function.

User Task:
This is a functional problem, you don't need to care about input, just complete the function bottomView() which should print the bottom view of the given tree.

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

Example:
Input:

2
2
1 3 L 1 2 R
8
4 5 L 4 4 R 5 2 L 5 7 R 4 -1 N 4 7 R 2 6 L 2 3 R
Output:
3 1 2
6 2 3 7 4 7

Explanation:
Testcase 1:
 
First case represents a tree with 3 nodes and 2 edges where root is 1, left child of 1 is 3 and right child of 1 is 2.

Thus nodes of the binary tree will be printed as such 3 1 2.


Note: The Input/Output format and Example 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 the 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
Author: kartik


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