An array $a$ is called ugly if it contains at least one element which is equal to the sum of all elements before it. If the array is not ugly, it is beautiful.

For example:

the array $[6, 3, 9, 6]$ is ugly: the element $9$ is equal to $6 + 3$;

the array $[5, 5, 7]$ is ugly: the element $5$ (the second one) is equal to $5$;

the array $[8, 4, 10, 14]$ is beautiful: $8 \ne 0$, $4 \ne 8$, $10 \ne 8 + 4$, $14 \ne 8 + 4 + 10$, so there is no element which is equal to the sum of all elements before it.

You are given an array $a$ such that $1 \le a_1 \le a_2 \le \dots \le a_n \le 100$. You have to reorder the elements of $a$ in such a way that the resulting array is beautiful. Note that you are not allowed to insert new elements or erase existing ones, you can only change the order of elements of $a$. You are allowed to keep the array $a$ unchanged, if it is beautiful.


-----Input-----

The first line contains one integer $t$ ($1 \le t \le 2000$) — the number of test cases.

Each test case consists of two lines. The first line contains one integer $n$ ($2 \le n \le 50$). The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_1 \le a_2 \le \dots \le a_n \le 100$).


-----Output-----

For each test case, print the answer as follows:

if it is impossible to reorder the elements of $a$ in such a way that it becomes beautiful, print NO;

otherwise, in the first line, print YES. In the second line, print $n$ integers — any beautiful array which can be obtained from $a$ by reordering its elements. If there are multiple such arrays, print any of them.


-----Examples-----

Input
4
4
3 3 6 6
2
10 10
5
1 2 3 4 5
3
1 4 4
Output
YES
3 6 3 6
NO
YES
2 4 1 5 3
YES
1 4 4


-----Note-----

None

Difficulty: EASY

Solutions:
import sys
input = sys.stdin.readline
for i in range(int(input())):
	input()
	a = [int(i) for i in input().split()]
	if a[0] == a[-1]:
		print('NO')
	else:
		print('YES')
		print(a[-1], ' '.join(list(map(str, a[:-1]))))


for _ in range(int(input())):
	n = int(input())
	a = list(map(int, input().split()))
	if a.count(a[0]) == len(a):
		print('NO')
	else:
		print('YES')
		mah = a.pop(a.index(max(a)))
		print(mah, ' '.join([str(x) for x in a]))


def reorder(array: list):
	max_element = array[-1]
	array.insert(0, max_element)
	return array[:-1]

def is_ugly(a):
	if a[0] == a[1]:
		return True
	else:
		return False

def list_to_string(array):
	array = [str(i) for i in array]
	return ' '.join(array)
t = int(input())
for _ in range(t):
	length = int(input())
	a = list(map(int, input().split()))
	reordered_a = reorder(a)
	if is_ugly(reordered_a):
		print('NO')
	else:
		print('YES')
		print(list_to_string(reordered_a))


for _ in range(int(input())):
	(_, arr) = (input(), sorted(map(int, input().split())))
	arr.insert(0, arr.pop())
	if arr[0] == arr[1]:
		print('NO')
	else:
		print(f"YES\n{' '.join(map(str, arr))}")


for tcase in range(int(input())):
	n = int(input())
	a = sorted(map(int, input().split()))
	b = [a.pop()]
	b += a
	if b[0] == b[1]:
		print('NO')
	else:
		print('YES')
		print(' '.join(map(str, b)))


t = int(input())
loo = []
for i in range(t):
	n = int(input())
	a = input().split()
	for j in range(n):
		a[j] = int(a[j])
	beauty = True
	if a[-1] == a[0]:
		beauty = False
	if beauty:
		loo.append(('YES', [a[-1]] + a[:len(a) - 1]))
	else:
		loo.append(('NO',))
for e in loo:
	if e[0] == 'YES':
		print(e[0])
		print(' '.join([str(e2) for e2 in e[1]]))
	else:
		print(e[0])


def reverse(seq, start, stop):
	size = stop + start
	for i in range(start, (size + 1) // 2):
		j = size - i
		(seq[i], seq[j]) = (seq[j], seq[i])
for i in range(int(input())):
	n = int(input())
	s = list(map(int, input().split()))
	s.sort(reverse=True)
	if len(set(s)) == 1:
		print('NO')
	else:
		print('YES')
		reverse(s, 1, len(s) - 1)
		print(' '.join(map(str, s)))


numbers = []
summ = 0
for i in range(int(input())):
	n = int(input())
	a = list(map(int, input().split(' ')))
	max_num = max(a)
	min_num = min(a)
	index_max = a.index(max(a))
	index_min = a.index(min(a))
	if len(set(a)) == 1:
		bool = 'NO'
		print(bool)
		continue
	bool = 'YES'
	numbers.append(max_num)
	numbers.append(min_num)
	a.remove(max_num)
	a.remove(min_num)
	numbers.extend(a)
	if bool == 'YES':
		print(bool)
		print(' '.join([str(i) for i in numbers]))
	numbers = []
	summ = 0


t = int(input())
for i in range(t):
	n = int(input())
	a = list(map(int, input().split(' ')))
	mina = 101
	maxa = 0
	for j in range(n):
		x = a[j]
		if x > maxa:
			maxa = x
		if x < mina:
			mina = x
	if mina == maxa:
		print('NO')
	else:
		print('YES')
		a.remove(maxa)
		a.remove(mina)
		print(maxa, mina, ' '.join(list(map(str, a))))