Running Median

You are given a stream of 'N' integers. For every 'i-th' integer added to the running list of integers, print the resulting median.

Print only the integer part of the median.

Input Format :

The first line of input contains an integer 'N', denoting the number of integers in the stream.

The second line of input contains 'N' integers separated by a single space.

Output Format :

Print the running median for every integer added to the running list in one line (space-separated).

Input Constraints

0 <= N <= 10 ^ 5
1 <= ARR[i] <= 10 ^ 5

Time Limit: 1 sec

Sample Input 1 :

6
6 2 1 3 7 5

Sample Output 1 :

6 4 2 2 3 4

Explanation of Sample Output 1 :

S = {6}, median = 6
S = {6, 2} -> {2, 6}, median = 4
S = {6, 2, 1} -> {1, 2, 6}, median = 2
S = {6, 2, 1, 3} -> {1, 2, 3, 6}, median = 2
S = {6, 2, 1, 3, 7} -> {1, 2, 3, 6, 7}, median = 3
S = {6, 2, 1, 3, 7, 5} -> {1, 2, 3, 5, 6, 7}, median = 4

Sample Input 2 :

5
5 4 3 2 1

Sample Output 2 :

5 4 4 3 3