Problem: You have array of n numbers a_{1}, a_{2}, …, a_{n}. 

Rearrange these numbers to satisfy |a_{1} - a_{2}| ≤ |a_{2} - a_{3}| ≤ … ≤ |a_{n-1} - a_{n}|, where |x| denotes absolute value of x. It's always possible to find such rearrangement.

Note that all numbers in a are not necessarily different. In other words, some numbers of a may be same.

You have to answer independent t test cases.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^{4}) — the number of test cases.

The first line of each test case contains single integer n (3 ≤ n ≤ 10^{5}) — the length of array a. It is guaranteed that the sum of values of n over all test cases in the input does not exceed 10^{5}.

The second line of each test case contains n integers a_{1}, a_{2}, …, a_{n} (-10^{9} ≤ a_{i} ≤ 10^{9}).

Output

For each test case, print the rearranged version of array a which satisfies given condition. If there are multiple valid rearrangements, print any of them.

Example

Input


2
6
5 -2 4 8 6 5
4
8 1 4 2


Output


5 5 4 6 8 -2
1 2 4 8

Note

In the first test case, after given rearrangement, |a_{1} - a_{2}| = 0 ≤ |a_{2} - a_{3}| = 1 ≤ |a_{3} - a_{4}| = 2 ≤ |a_{4} - a_{5}| = 2 ≤ |a_{5} - a_{6}| = 10. There are other possible answers like "5 4 5 6 -2 8".

In the second test case, after given rearrangement, |a_{1} - a_{2}| = 1 ≤ |a_{2} - a_{3}| = 2 ≤ |a_{3} - a_{4}| = 4. There are other possible answers like "2 4 8 1".

Solution (in PYTHON3):

Solution:

t=int(input())
fl=[]
for i in range(t):
    n=int(input())
    s=input()
    l=s.split(' ')
    for i in range(n):
        l[i]=int(l[i])
    fl.append(l)
#fl=[[5,-2,4,8,6,5],[8,1,4,2]]
#print(fl)
fll=[]
for ii in fl:
    i=ii[:]
    i.sort()
    ll=[]
    f=0
    while(len(i)!=0):
        #print(i)
        if(f==1):
            #print('.')
            ll.append(i[len(i)-1])
            i.pop(len(i)-1)
            f=0
        else:
            #print('..')
            ll.append(i[0])
            i.pop(0)
            f=1
    ll.reverse()
    fll.append(ll)
#print(fll)
for i in range(len(fll)):
    for j in range(len(fll[i])):
        fll[i][j]=str(fll[i][j])
ssl=[]
for i in fll:
    ss=" ".join(i)
    ssl.append(ss)
#print(ssl)
for i in ssl:
    print(i)