Given an input stream of N integers. The task is to insert these numbers into a new stream and find the median of the stream formed by each insertion of X to the new stream.

Input:
The first line of input contains an integer N denoting the number of elements in the stream. Then the next N lines contains integer x denoting the number to be inserted into the stream.
Output:
For each element added to the stream print the floor of the new median in a new line.
 
Constraints:
1 <= N <= 106
1 <= x <= 106
 
Example:
Input:
4
5
15

3
Output:
5
10
5
4
 
Explanation:
Testcase 1:
Flow in stream : 5, 15, 1, 3
5 goes to stream --> median 5 (5)
15 goes to stream --> median 10 (5, 15)
1 goes to stream --> median 5 (5, 15, 1)
3 goes to stream --> median 4 (5, 15, 1, 3)
 

** For More Input/Output Examples Use 'Expected Output' option **

Author: Shubham Joshi 1


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