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:
The first line of input contains T denoting number of testcases. T testcases follow. Each testcase contains two lines of input. The first line contains the number of edges. The second line contains the relation between nodes.

Output Format:
The function should print nodes in 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 funcitonal 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<= 30
0 <= Number of nodes <= 100
0 <= Data of a node <= 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:
3 1 2
40 20 60 30

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 binary tree will be printed as such 3 1 2.
 

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

Contributor: Amit Khandelwal
Author: kartik


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