### COCI 2008/2009, Contest #3

## Task BST

A binary search tree is a tree in which every node has **at most** two child nodes (a left and a right child). Each node had an integer written insude it. If the number `X`

is written inside a node, then the numbers in its left subtree are less than `X`

and the numbers in its right subtree are greater than `X`

.

You will be given a sequence of integers between 1 and `N`

such that each number appears in the sequence exactly *once*. You are to create a binary search tree from the sequence, putting the first number in the root node and inserting every other number in order. In other words, run `insert( X, root )`

for every other number:

insert( number X, node N ) increase the counter C by 1 if X is less than the number in node N if N has no left child create a new node with the number X and set it to be the left child of node N else insert( X, left child of node N ) else (X is greater than the number in node N) if N has no right child create a new node with the number X and set it to be the right child of node N else insert( X, right child of node N )

Write a program that calculates the value of `C`

after every number is inserted. You may assume the counter is initially 0.

### Input

The first line contains the integer `N`

(1 ≤ `N`

≤ 300 000), the length of the sequence.

The remaining `N`

lines contain the numbers in the sequence, integers in the interval [`1..N`

]. The numbers will be distinct.

### Output

Output `N`

integers each on its own line, the values of the counter `C`

after each number is inserted into the tree.

### Scoring

In test cases worth 50% of points, `N`

will be at most 1000.

### Examples

## Input4 1 2 3 4 ## Output0 1 3 6 |
## Input5 3 2 4 1 5 ## Output0 1 2 4 6 |
## Input8 3 5 1 6 8 7 2 4 ## Output0 1 2 4 7 11 13 15 |

All Submissions

Best Solutions

**Point Value:** 20 (partial)

**Time Limit:** 2.00s

**Memory Limit:** 32M

**Added:** Dec 13, 2008

**Languages Allowed:**

C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

## Comments (Search)

competitivecoderon Nov 07, 2015 - 11:13:42 am UTC TLE even after correct algorithmjargonon Nov 07, 2015 - 5:34:54 pm UTC Re: TLE even after correct algorithmIn general, if the problem has more than about 20 accepted users, the problem itself is probably fine.

competitivecoderon Nov 08, 2015 - 5:19:01 am UTC Re: TLE even after correct algorithmmagicalsoupon Jul 13, 2018 - 2:54:06 pm UTC Re: TLE even after correct algorithmhansonw1on Jan 03, 2009 - 5:32:43 pm UTC Re: OutputAll the other numbers are inserted normally, though.