Given an input stream of n integers the task is to insert integers to stream and print the median of the new stream formed by each insertion of x to the stream.

Example

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)

**Input:**

The first line of input contains an integer N denoting the no of elements of the stream. Then the next N lines contains integer x denoting the no to be inserted to the stream.

**Output:**

For each element added to the stream print the floor of the new median in a new line.

**Constraints:**

1<=N<=10^5+7

1<=x<=10^5+7

**Example:**

Input:

4

5

15

1

3

**Output:**

5

10

5

4

#### **For More Examples Use Expected Output**