RMID2 - Running Median Again


Danish has just solved the problem Running Median.

The first line of the problem says "You will be given some integers in non-decreasing order". The problem asks you to report and remove the median of the list every time it is queried.

Having solved this problem, Danish now begins to wonder how to solve the problem if the input is in any order (not necessarily non-decreasing order as mentioned above).

Can you help him?

Your task is to take as input a list of positive integers. Whenever -1 is given as input, you must output the median of the list, and remove it from the list. Take the smaller element as the median in case of even number of elements.

Input

The input contains several test caes.

The first line contains an integer t, the number of test cases.

Each test case has several lines, each containing an integer n (<=10^9) . If n is positive, add it to the list. n=-1 indicates a median query (there will be no median query if the list is empty). The test case is terminated by n=0.

In each test case, there will be upto 10^5 integers to be added to the list, and upto 10^5 median queries.

Output

For each median query as described above, print the median on a new line.

Example

Input:
1
9
10
2
5
1
18
-1
-1
4
3
-1
8
7
-1
0

Output:
5
9
3
7

hide comments
be1035016: 2018-06-17 18:13:18

O(nlogn) accepted.used fast i/o with cin/cout.good problem.took lots of thinking

chetan101: 2018-04-26 19:35:45

Use printf/scanf instead of cin\cout.

charraster: 2018-04-15 13:54:16

Just solved. You have to use fast buffered IO. I am reading 512bytes at a time, and writing in batches of 32 integers.

coolyansh: 2018-03-22 08:27:14

The required time complexity is O(n log n). Even if the solution is of the required complexity TLE or WA can occur because of the following reasons:
1. Use printf/scanf instead of cin/cout for faster execution as the time limit is very strict
2. Don't forget to print an additional \n after each test case

avjot_singh99: 2018-03-01 09:53:56

Accepted in 0.20s
Try getchar_unlocked() and putchar_unlocked() for faster I/O. Made a huge difference

Last edit: 2018-03-01 10:17:21
anhtuan_77: 2018-01-30 14:47:55

TLE :(

v_pp_27: 2017-12-15 07:50:21

after lots WAs, runtime errors,tle ...finally solved it.... : ).

Last edit: 2017-12-15 07:54:24
snitesh24: 2017-12-12 17:59:17

nlogn accepted after replacing cin with getchar_unlocked() in .92 secs

kshubham02: 2017-12-06 13:35:31

O(n logn) giving TLE???? What is expected time complexity?

Aditya NK: 2017-12-06 09:41:03

Please Note that number of integer in the input is greater than 10^5 but less than 10^6. Cost me a lot of WA and time.


Added by:Akhilesh Anandh
Date:2013-10-05
Time limit:0.100s-0.695s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:variation on RMID