Binary Search Tree

Time Limit: 10 Seconds    Memory Limit: 65536 KB

A binary search tree is a binary tree that satisfies the following properties:

  • The left subtree of a node contains only nodes with keys less than the node's key.
  • The right subtree of a node contains only nodes with keys greater than the node's key.  
  • Both the left and right subtrees must also be binary search trees.

http://sharecode.ir/assets/problem_images/1353_a60ea8e2a625a8b30eba5c6095803164.jpg

Pre-order traversal (Root-Left-Right) prints out the node’s key by visiting the root node then traversing the left subtree and then traversing the right subtree. Post-order traversal (Left – Right-Root)  prints out the left subtree first and then right subtree and finally the root node. For example, the results of pre-order traversal and post-order traversal of the binary tree shown in
Figure 1 are as follows: 

Pre-order:  50, 30, 24, 5, 28, 45, 98, 52, 60  
Post-order:  5, 28, 24, 45, 30, 60, 52, 98, 50

Given the pre-order traversal of a binary search tree, you task is to find the post-order traversal of this tree.

Input

The keys of all nodes of the input binary search tree are given according to pre-order traversal. Each node has a key value which is a positive integer less than 1000000. All values are given in separate lines (one integer per line). You can assume that a binary search tree does not contain more than 10,000 nodes and there are no duplicate nodes.

Output

The output contains the result of post-order traversal of the input binary tree. Print out one key per line.

Sample Input

50 
30 
24 
5 
28 
45 
98
52
60

Sample Output

5 
28 
24 
45 
30 
60 
52 
98 
50
Submit

Source: ACM ICPC Asia Regional 2011 Phuket Site