Algorithms and Data Structures

Performing Queries on a Binary Search Tree

Given an empty binary search tree with no nodes, you are asked to perform 3 kinds of queries:
  1. insert x - insert the value x in the BST
  1. search x - check if the value x is in the BST
  1. print - print the BST in the in-order traversal order.
Given q queries, you are asked to write a program to perform these queries.

Input

The first line of the input contains a single number q (1 ≤ q ≤ 1000).
The next q lines contain queries. For all the insert and search queries the value of x does not exceed in absolute value.

Output

For each search query, the program should print Yes if the value is present in the BST, and No otherwise on a new line.
For each print query, the program should print the in-order traversal of the BST, where the values should be separated by a space.

Examples

Input
Output
6 insert 2 insert 1 search 3 insert 0 print search 1
No 0 1 2 Yes
 

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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