MKnez wants to construct an array $s_1,s_2, \ldots , s_n$ satisfying the following conditions:

Each element is an integer number different from $0$;

For each pair of adjacent elements their sum is equal to the sum of the whole array.

More formally, $s_i \neq 0$ must hold for each $1 \leq i \leq n$. Moreover, it must hold that $s_1 + s_2 + \cdots + s_n = s_i + s_{i+1}$ for each $1 \leq i < n$.

Help MKnez to construct an array with these properties or determine that it does not exist.


-----Input-----

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \leq t \leq 100$). The description of the test cases follows.

The only line of each test case contains a single integer $n$ ($2 \leq n \leq 1000$) — the length of the array.


-----Output-----

For each test case, print "YES" if an array of length $n$ satisfying the conditions exists. Otherwise, print "NO". If the answer is "YES", on the next line print a sequence $s_1,s_2, \ldots, s_n$ satisfying the conditions. Each element should be a non-zero integer in the range $[-5000,5000]$, i. e. $-5000 \leq s_i \leq 5000$ and $s_i \neq 0$ should hold for each $1 \leq i \leq n$.

It can be proved that if a solution exists then there also exists one which satisfies the additional constraints on the range.

If there are several correct answers, print any of them.


-----Examples-----

Input
2
2
3
Output
YES
9 5
NO


-----Note-----

In the first test case, $[9,5]$ is a valid answer since $9+5$ (the sum of the two adjacent elements $s_1+s_2$) is equal to $9+5$ (the sum of all elements). Other solutions include $[6,-9], [-1,-2], [-5000,5000], \ldots$

For the second test case, let us show why some arrays do not satisfy the constraints:

$[1,1,1]$  — $s_1+s_2 = 1+1 = 2$ and $s_1+s_2+s_3=1+1+1 = 3$ differ;

$[1,-1,1]$  — $s_1+s_2=1+(-1)=0$ and $s_1+s_2+s_3=1+(-1)+1 = 1$ differ;

$[0,0,0]$  — The array $s$ cannot contain a $0$.

This is not a proof, but it can be shown that the answer is "NO".

Difficulty: EASY

Solutions:
def solution(n):
	if n % 2 == 0:
		print('YES')
		print('1 -1 ' * (n // 2))
	else:
		na = (n - 1) // 2
		nb = na - 1
		if nb == 0:
			print('NO')
			return
		else:
			print('YES')
			a = nb
			b = -na
			print(f'{a} {b} ' * na + f'{a}')
t = int(input())
for _ in range(t):
	n = int(input())
	solution(n)


for _ in range(int(input())):
	n = int(input())
	if n % 2 == 0:
		print('YES')
		print('1 -1 ' * (n // 2))
	elif n > 3:
		x = (n - 1) // 2
		print('YES')
		print((str(x - 1) + ' ' + str(-x) + ' ') * (n // 2) + str(x - 1))
	else:
		print('NO')


class Solution:

	def solve(n: int):
		if n == 3:
			print('NO')
			return
		print('YES')
		if not n % 2:
			print('1 -1 ' * int(n // 2))
			return
		positive = int((n - 3) / 2)
		negative = '-' + str(int(positive + 1))
		result = (str(positive) + ' ' + negative + ' ') * int(n // 2) + str(positive)
		print(result)

	def MKnezTask():
		for i in range(int(input())):
			size = int(input())
			Solution.solve(size)
Solution.MKnezTask()


for _ in range(int(input())):
	n = int(input())
	if n == 3:
		print('NO')
		continue
	print('YES')
	if n % 2 == 0:
		print('1 -1 ' * (n // 2))
	else:
		a = (n - 3) // 2
		b = -a - 1
		print(f'{a} {b} ' * (n // 2) + f'{a}')


def fnc(n):
	if n == 3:
		return 'NO'
	elif n % 2 == 0:
		print('YES')
		return int(n / 2) * '1 -1 '
	else:
		a = int((n - 1) / 2)
		b = int((3 - n) / 2)
		c = str(b) + ' ' + str(a) + ' '
		print('YES')
		return a * c + str(b)
n = int(input())
for i in range(0, n):
	x = int(input())
	print(fnc(x))


for _ in range(int(input())):
	n = int(input())
	if n % 2 == 0:
		t = ''
		print('YES')
		for __ in range(n // 2):
			t += '1 -1 '
		print(t)
	elif n == 3:
		print('NO')
	else:
		print('YES')
		t = ''
		for i in range(n // 2):
			t += str(1 - n // 2) + ' ' + str(n // 2) + ' '
		t += str(1 - n // 2)
		print(t)


n = int(input())
for i in range(n):
	x = int(input())
	ans = ''
	if x % 2 == 0:
		print('YES')
		for j in range(x):
			if j % 2 == 0:
				ans += '1 '
			else:
				ans += '-1 '
		print(ans)
	elif x == 3:
		print('NO')
	else:
		y = x // 2
		z = 1 - y
		print('YES')
		for k in range(x):
			if k % 2 == 0:
				ans += str(z)
				ans += ' '
			else:
				ans += str(y)
				ans += ' '
		print(ans)


import math
for _ in range(int(input())):
	n = int(input())
	if n % 2 == 0:
		s = ''
		for i in range(n // 2):
			s += '1 -1' + ' '
		print('YES')
		print(s)
	elif n == 3:
		print('NO')
	else:
		s = ''
		for i in range(n // 2):
			s += str((n // 2 - 1) * -1) + ' ' + str(n // 2) + ' '
		s += str((n // 2 - 1) * -1)
		print('YES')
		print(s)


import math
t = int(input())
for i in range(t):
	n = int(input())
	if n == 3:
		print('NO')
	else:
		print('YES')
		s = ''
		if n % 2 == 0:
			n1 = 1
			n2 = -1
			s = ''
			for i in range(n):
				if i % 2 == 0:
					s += str(n1) + ' '
				else:
					s += str(n2) + ' '
		else:
			n1 = -1 * (n // 2)
			n2 = n // 2 - 1
			s = ''
			for i in range(n):
				if i % 2 == 0:
					s += str(n2) + ' '
				else:
					s += str(n1) + ' '
		print(s)


def solve():
	n = int(input())
	if n == 3:
		out = 'NO'
	else:
		out = 'YES\n'
		(a, b) = (1, -1)
		if n % 2 != 0:
			a = int((n - 1) / 2 - 1)
			b = int((1 - n) / 2)
		for i in range(0, n):
			if i % 2 == 0:
				out += str(a)
			else:
				out += str(b)
			out += ' '
	print(out)
t = int(input())
for i in range(0, t):
	solve()


def solve():
	n = int(input())
	s = ''
	if n % 2 == 0:
		print('YES')
		while n:
			a = (-1) ** n
			s = f'{s}{a} '
			n -= 1
		print(s)
	elif n == 3:
		print('NO')
	else:
		a = int((n - 1) / 2 - 1)
		b = int(-((n - 1) / 2))
		n -= 1
		s = f'{a} '
		while n:
			s = f'{s}{b} {a} '
			n -= 2
		print('YES')
		print(s)
t = 1
t = int(input())
while t:
	solve()
	t -= 1


for i in range(int(input())):
	n = int(input())
	s = ''
	if n == 3:
		print('NO')
		continue
	if n % 2 != 0:
		for i in range(n):
			if i % 2 == 0:
				s += str(-(int(n / 2) - 1)) + ' '
			else:
				s += str(int(n / 2)) + ' '
	else:
		for i in range(n):
			if i % 2 == 0:
				s += '1 '
			else:
				s += '-1 '
	print('YES')
	print(s)


t = int(input())
for i in range(t):
	n = int(input())
	if n == 3:
		print('NO')
	elif n % 2 == 0:
		print('YES')
		s = ''
		for j in range(int(n / 2)):
			s += '1 '
			s += '-1 '
		print(s)
	elif n % 2 != 0:
		print('YES')
		k = int(int(n) / int(2))
		s = ''
		for j in range(int(n / 2)):
			s += str(k - 1)
			s += ' '
			s += str(-k)
			s += ' '
		s += str(k - 1)
		print(s)


test = int(input())
while test:
	n = int(input())
	if n == 3:
		print('NO')
	else:
		print('YES')
		if n % 2 == 0:
			a = 1
			b = -1
			for i in range(n // 2):
				print(a, b, end=' ')
			print()
		else:
			a = -((n - 2) // 2)
			s = 1
			for i in range(n // 2):
				print(a, s - a, end=' ')
			print(a)
	test -= 1