Problem: Sayaka Saeki is a member of the student council, which has n other members (excluding Sayaka). The i-th member has a height of a_i millimeters.

It's the end of the school year and Sayaka wants to take a picture of all other members of the student council. Being the hard-working and perfectionist girl as she is, she wants to arrange all the members in a line such that the amount of photogenic consecutive pairs of members is as large as possible.

A pair of two consecutive members u and v on a line is considered photogenic if their average height is an integer, i.e. (a_u + a_v)/(2) is an integer.

Help Sayaka arrange the other members to maximize the number of photogenic consecutive pairs.

Input

The first line contains a single integer t (1≤ t≤ 500) — the number of test cases.

The first line of each test case contains a single integer n (2 ≤ n ≤ 2000) — the number of other council members.

The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2 ⋅ 10^5) — the heights of each of the other members in millimeters.

It is guaranteed that the sum of n over all test cases does not exceed 2000.

Output

For each test case, output on one line n integers representing the heights of the other members in the order, which gives the largest number of photogenic consecutive pairs. If there are multiple such orders, output any of them.

Example

Input


4
3
1 1 2
3
1 1 1
8
10 9 13 15 3 16 9 13
2
18 9


Output


1 1 2 
1 1 1 
13 9 13 15 3 9 16 10 
9 18 

Note

In the first test case, there is one photogenic pair: (1, 1) is photogenic, as (1+1)/(2)=1 is integer, while (1, 2) isn't, as (1+2)/(2)=1.5 isn't integer.

In the second test case, both pairs are photogenic.

Solution (in PYTHON3):

Solution:
import collections
import itertools
from functools import reduce

mod = (10 ** 9) + 7


def permutationbysum():
    for _ in range(int(input())):
        num, l, r, achieve = map(int, input().split())
        k = r - l + 1
        if (k * (k + 1)) // 2 <= achieve <= (k * (num * 2 + 1 - k)) // 2:
            outpos = (r) % num
            inpos = l - 1
            ans = [0] * num
            for i in range(num, 0, -1):
                if achieve - i > 0 or (achieve - i == 0 and inpos == r - 1):
                    achieve -= i
                    ans[inpos] = i
                    inpos += 1
                else:
                    ans[outpos] = i
                    outpos += 1
                    outpos %= num
            print(*ans)
        else:
            print(-1)


# permutationbysum()

def peaks():
    for _ in range(int(input())):
        num, peak = map(int, input().split())
        pos = 1
        rpos = num
        ans = []
        now = 0
        if num == 1:
            if not peak:
                print(1)
            else:
                print(-1)
            continue
        if num == 2:
            if peak:
                print(-1)
            else:
                print(1, 2)
            continue
        added = 0
        while rpos + 1 != pos:
            if not peak:
                while pos <= rpos:
                    ans.append(pos)
                    pos += 1
                break
            if not now:
                ans.append(pos)
                pos += 1
            else:
                ans.append(rpos)
                rpos -= 1
                if num - added != 1:
                    peak -= 1
            added += 1
            now = 1 - now
        if peak:
            print(-1)
            continue
        print(*ans)


# peaks()
import sys

input = sys.stdin.readline


def addone():
    for _ in range(int(input())):
        num, changes = input().split()
        l = collections.deque(sorted([int(i) for i in num]))
        perm = collections.deque()
        changes = int(changes)
        cd = 0
        ans = len(num)
        while True:
            nextnum = l.pop()
            while perm and perm[-1] == nextnum:
                l.append(perm.pop())
            c = (10 - nextnum) - cd
            changes -= c
            cd += c
            if changes >= 0:
                if not c:
                    perm.appendleft(1 - cd)
                    l.appendleft(-cd)
                else:
                    l.appendleft(1 - cd)
                    l.appendleft(-cd)
                ans += 1
            else:
                break
        print(ans % 1000000007)


# addone()

import math


def andsequences():
    def mapping(num):
        nonlocal mnum
        nonlocal c
        num = int(num)
        if num < mnum:
            mnum = num
            c = 1
        elif num == mnum:
            c += 1
        return num

    mod = 1000000007
    for _ in range(int(input())):
        mnum = float('inf')
        c = 0
        num = int(input())
        l = list(map(mapping, input().split()))
        for i in l:
            if mnum & i != mnum:
                print(0)
                break
        else:
            if c == 1:
                print(0)
            else:
                print((math.factorial(num - 2) * (c - 1) * c) % mod)


# andsequences()

def numberdigit():
    n = ((10 ** 5) * 2)
    l = [0] * 11
    mod = 10 ** 9 + 7
    l[0] = l[1] = l[2] = l[3] = l[4] = l[5] = l[6] = l[7] = l[8] = 2
    l[9] = 3
    l[10] = 4
    for i in range(11, n):
        l.append((l[i - 10] + l[i - 9]) % mod)
    for _ in range(int(input())):
        num, c = input().split()
        c = int(c)
        ans = 0
        for i in num:
            i = int(i)
            if 10 - i > c:
                ans += 1
            else:
                ans += l[c - (10 - i)]
        print(ans % mod)


# numberdigit()

def mushroom():
    people, t1, t2, percent = map(int, input().split())
    l = []
    percent = 1 - percent * 0.01
    for i in range(1, people + 1):
        s, s1 = map(int, input().split())
        l.append([i, max(s * t1 * percent + s1 * t2, s1 * t1 * percent + s * t2)])
    l.sort(key=lambda x: (x[1]), reverse=True)
    for i in l:
        i[1] = "{:.2f}".format(i[1])
        print(*i)


# mushroom()

def escape():
    prins = int(input())
    dra = int(input())
    start = int(input())
    pack = int(input())
    c = int(input())
    speeddiff = dra - prins
    if speeddiff <= 0:
        return 0
    pd = start * prins
    ans = 0
    while pd < c:
        hs = pd / speeddiff
        pd += prins * hs
        if pd >= c:
            break
        time = pd / dra
        time += pack
        pd += prins * time
        ans += 1
    return ans


# print(escape())

def perm():
    def high(n, k):
        return k * (2 * n - k + 1) // 2

    def low(k):
        return k * (k + 1) // 2

    for _ in range(int(input())):
        num, lef, rig, s = map(int, input().split())
        k = rig - lef + 1
        rig, lef = rig - 1, lef - 1
        if not high(num, k) >= s >= low(k):
            print(-1)
            continue
        l = [0] * num
        lp = lef
        rp = lef - 1
        for i in range(num, 0, -1):
            if high(i, k) >= s and s - i >= low(k - 1) and k:
                l[lp] = i
                lp += 1
                s -= i
                k -= 1
            else:
                l[rp] = i
                rp -= 1
        if k:
            print(-1)
        else:
            print(*l)


# perm()


def newcom():
    for _ in range(int(input())):
        days, price = map(int, input().split())
        dl = input().split()
        worth = input().split()
        worth.append(0)
        ans = float('inf')
        req = 0
        left = 0
        for i in range(days):
            a = int(dl[i])
            w = int(worth[i])
            ans = min(ans, req + max(0, price - left + a - 1) // a)
            ns = max(0, w - left + a - 1) // a
            req += ns + 1
            left += a * ns - w
        print(ans)


# newcom()


def perfectsq():
    for _ in range(int(input())):
        n = input()
        for i in input().split():
            sq = math.sqrt(int(i))
            if sq != int(sq):
                print("YES")
                break
        else:
            print("NO")


# perfectsq()

def and0big():
    for _ in range(int(input())):
        l, k = map(int, input().split())
        print(l ** k % mod)


# and0big()

import math


def mod1p():
    n = int(input())
    ans = dict()
    p = 1
    for i in range(1, n):
        if math.gcd(i, n) == 1:
            ans[str(i)] = True
            p = (p * i) % n
    if p == 1:
        print(len(ans))
        print(' '.join(ans.keys()))
    else:
        ans.pop(str(p))
        print(len(ans))
        print(' '.join(ans.keys()))


# mod1p()

def shorttask():
    num = 10000100
    l = [-1] * (num + 2)
    s = [-1] * (num + 2)
    l[1] = 1
    for i in range(2, int(math.sqrt(num + 1)) + 2):
        if l[i] == -1:
            l[i] = i
            for x in range(i * i, num + 1, i):
                if l[x] == -1:
                    l[x] = i
    s[1] = 1
    for i in range(2, num + 1):
        if l[i] == -1:
            l[i] = i
            s[i] = i + 1
        else:
            i1 = i
            s[i] = 1
            while i1 % l[i] == 0:
                i1 //= l[i]
                s[i] = s[i] * l[i] + 1
            s[i] *= s[i1]
    ans = [-1] * (num + 1)
    for i in range(num, 0, -1):
        if s[i] < num:
            ans[s[i]] = i
    for _ in range(int(input())):
        print(ans[int(input())])


# shorttask()

def review():
    for _ in range(int(input())):
        n = int(input())
        ans = 0
        for i in input().split():
            i = int(i)
            if i == 1 or i == 3:
                ans += 1
        print(ans)


# review()

def GCDleng():
    po10 = [0] * 11
    po10[1] = 1
    for i in range(2, 11):
        po10[i] = po10[i - 1] * 10
    for _ in range(int(input())):
        n, n1, res = map(int, input().split())
        print(po10[n], po10[n1] + po10[res])


# GCDleng()


def anothercarddeck():
    n, q = map(int, input().split())
    l = input().split()
    d = {l[i]: i for i in range(n - 1, -1, -1)}
    ans = []
    for i in input().split():
        now = d[i]
        ans.append(now + 1)
        for key in d:
            if d[key] < now:
                d[key] += 1
        d[i] = 0
    print(*ans)


# anothercarddeck()

def mincoststring():
    n, letters = map(int, input().split())
    l = [chr(i + 97) for i in range(letters)]
    ans = []
    real = letters - 1
    if not n:
        print(*ans, sep='')
        return
    if n == 1:
        print(*ans, sep='', end='')
        print(l[1 % (real + 1)])
        return
    while n:
        for i in range(len(l)):
            for i1 in range(i, len(l)):
                if i1 != real:
                    ans.append(l[i1])
                    ans.append(l[i])
                    n -= 2
                else:
                    ans.append(l[i1])
                    n -= 1
                if not n:
                    print(*ans, sep='')
                    return
                if n == 1:
                    print(*ans, sep='', end='')
                    print(l[(i1 + 1) % (real + 1)])
                    return
    print(*ans)


# mincoststring()


def mincost2():
    n, letters = map(int, input().split())
    l = [chr(i + 97) for i in range(letters)]
    comb = []
    if letters == 1 or n == 1:
        print('a' * n)
        return
    for i in range(letters):
        for i1 in range(i, letters):
            comb.append(l[i1] + l[i])
    lc = len(comb)
    while True:
        for i in range(lc):
            if ord(comb[i][0]) - 97 == letters - 1:
                n -= 1
                print(comb[i][0], end='')
            else:
                n -= 2
                print(comb[i], end='')
            if n == 1:
                pos = ord(comb[i][0]) - 97 + 1
                print(l[pos % letters])
                return
            if not n:
                return


# mincost2()
def Tittat():
    for _ in range(int(input())):
        n, k = map(int, input().split())
        l = list(map(int, input().split()))
        for i in range(n):
            if not k:
                break
            while k and l[i]:
                l[i] -= 1
                l[-1] += 1
                k -= 1
        print(*l)


# Tittat()

def xorq2():
    for _ in range(int(input())):
        n = int(input())
        s = 0
        num = -1
        nc = 0
        c = 0
        for i in input().split():
            i = int(i)
            s ^= i
            c += 1
            if num == -1 and s == i:
                num = s
                s = 0
                nc += c
                c = 0
            if num != -1 and (s == num or not s):
                s = 0
                nc += c
                c = 0
        print(['NO', 'YES'][nc == n])


# xorq2()


def xorq2re():
    n = int(input())
    s = input().split()
    xor = 0
    for i in range(n):
        s[i] = int(s[i])
        xor ^= s[i]
    if not xor:
        print("YES")
    else:
        new = 0
        ans = 0
        for i in s:
            new ^= i
            if new == xor:
                new = 0
                ans += 1
        print(["NO", "YES"][ans > 1])


import sys

sys.setrecursionlimit(2300)


def q3partition():
    def partition():
        if tol % 2:
            return 0
        up = tol
        rec = [[False] * (up + 2) for _ in range(n + 1)]
        rec[0][0] = True
        for i in range(1, n + 1):
            v = l[i - 1]
            for j in range(up + 1):
                if rec[i - 1][j]:
                    if v + j <= up:
                        rec[i][j + v] = True
                    rec[i][j] = True

        return rec[n][tol//2]

    def ints(x):
        nonlocal tol
        nonlocal gcf
        x = int(x)
        tol += x
        gcf = math.gcd(gcf,x) if gcf != float('inf') else x
        return x

    n = int(input())
    tol = 0
    gcf = float('inf')
    l = list(map(ints, input().split()))
    if partition():
        pos = 1
        for i in l:
            if i // gcf % 2:
                print(1)
                print(pos)
                return
            pos += 1
    else:
        print(0)


def main():
    # for _ in range(int(input())):
    q3partition()


# main()
def permu(n,r):
    return math.factorial(n) // math.factorial(n-r)
def comb(n,r):
    return math.factorial(n) // math.factorial(r)*math.factorial(n-r)
def calc():
    n = int(input())
    ans = permu(n,n)
    for i in range(1,n+1):
        ans -= comb(n,i)
    print(ans)
# calc()



def order():
    for _ in range(int(input())):
        n = int(input())
        odd = []
        even = []
        for i in input().split():
            i = int(i)
            if i % 2:
                odd.append(i)
            else:
                even.append(i)
        print(*odd+even)
order()