EC_ESTA - Statistics Applied

In this problem we will be looking for medians of data set. Median is the central element in ordered data group. For example: for the set {2, 6, 3, 3, 2} the median would be 3. In general, if we have n elements {a1, a2, a3 ... an}, we define the median as element a(n+1)/2 if n is odd and (an/2+an/2+1)/2 otherwise.

You will be given N numbers and you must calculate N medians. i-th median is taken on the subset [a1, a2, a3 ... ai] for 1 ≤ i ≤ N.

Input

The first line contains the number of test cases. Each case consists of an integer N (1 ≤ N ≤ 100000). N integers ai (0 ≤ ai < 231) follow, elements in data set.

Output

For each case, print N lines with the medians. If the result is non-integral, print the exact value using decimal point (see example).

Example

Input:
2
4
3 5 7 3
2
3 4

Output:
3
4
5
4
3
3.5

Added by:Eddy Cael
Date:2013-10-26
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:C C++ 4.3.2 CPP JAVA
Resource:COMPETENCIA CCBOL2013

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