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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.

**Example 1:**

**Input:
** 1
/ \
3 2
**Output: **3 1 2**
Explanation:**
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.

**Example 2:**

**Input:
** 10
/ \
20 30
/ \
40 60
**Output: **40 20 60 30

**Your Task:**

This is a functional problem, you **don't **need to care about input, just complete the function **bottomView**() which takes the root node of the tree as input and returns an array containing the bottom view of the given tree.

**Expected Time Complexity: **O(N).

**Expected Auxiliary Space: **O(N).

**Constraints:**

1 <= Number of nodes <= 10^{5}

1 <= Data of a node <= 10^{5}

**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.

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Bottom View of Binary Tree

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