Pre-order traversal of a binary tree

Pre-order traversal of a tree is a recursive procedure, where you first visit a node, then visit its left subtree, then visit its right subtree:

Visit the current node

Visit the left subtree (node.left)

Visit the right subtree (node.right)

Given a binary tree, you are asked to perform a pre-order traversal on it.

Input

The input contains space-separated integers representing the values in the nodes of the binary tree. The order of the values is given as described in the previous statement (by traversing from the left to the right subtree every time). A value of 0 means that the node does not exist. It’s guaranteed that the input binary tree is valid.

Output

The program should print the values in the nodes of a binary tree when performing a pre-order traversal. All the values should be separated by a space.

Examples

Input	Output
1 2 3 4 5 8 9 0 0 0 0 0 0 6 7 0 0 0 0	1 2 4 8 9 5 3 6 7
1 2 3 4 5 8 0 0 0 0 0 6 7 0 0 0 0	1 2 4 8 5 3 6 7
1 2 3 4 5 0 0 0 0 6 7 0 0 8 9 0 0 0 0	1 2 4 5 3 6 7 8 9
1 2 3 4 5 0 0 7 8 0 0 0 0 0 6 0 0	1 2 4 5 7 8 3 6

Explanation

Example 1:

Example 2:

Example 3:

Example 4:

Pre-order traversal of a binary tree

Input

Output

Examples

Explanation

Constraints

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