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 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 denotes 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:
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.

Your 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<= 30
1 <= Number of nodes <= 105
1 <= Data of a node <= 105

Example:
Input:

2
1 3 2
10 20 30 40 60

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 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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