There are $n$ participants in a competition, participant $i$ having a strength of $s_i$.

Every participant wonders how much of an advantage they have over the other best participant. In other words, each participant $i$ wants to know the difference between $s_i$ and $s_j$, where $j$ is the strongest participant in the competition, not counting $i$ (a difference can be negative).

So, they ask you for your help! For each $i$ ($1 \leq i \leq n$) output the difference between $s_i$ and the maximum strength of any participant other than participant $i$.


-----Input-----

The input consists of multiple test cases. The first line contains an integer $t$ ($1 \leq t \leq 1000$) — the number of test cases. The descriptions of the test cases follow.

The first line of each test case contains an integer $n$ ($2 \leq n \leq 2\cdot10^5$) — the length of the array.

The following line contains $n$ space-separated positive integers $s_1$, $s_2$, ..., $s_n$ ($1 \leq s_i \leq 10^9$) — the strengths of the participants.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot10^5$.


-----Output-----

For each test case, output $n$ space-separated integers. For each $i$ ($1 \leq i \leq n$) output the difference between $s_i$ and the maximum strength of any other participant.


-----Examples-----

Input
5
4
4 7 3 5
2
1 2
5
1 2 3 4 5
3
4 9 4
4
4 4 4 4
Output
-3 2 -4 -2 
-1 1 
-4 -3 -2 -1 1 
-5 5 -5 
0 0 0 0


-----Note-----

For the first test case:

The first participant has a strength of $4$ and the largest strength of a participant different from the first one is $7$, so the answer for the first participant is $4 - 7 = -3$.

The second participant has a strength of $7$ and the largest strength of a participant different from the second one is $5$, so the answer for the second participant is $7 - 5 = 2$.

The third participant has a strength of $3$ and the largest strength of a participant different from the third one is $7$, so the answer for the third participant is $3 - 7 = -4$.

The fourth participant has a strength of $5$ and the largest strength of a participant different from the fourth one is $7$, so the answer for the fourth participant is $5 - 7 = -2$.

Difficulty: EASY

Solutions:
t = int(input())
for x in range(t):
	n = input()
	s = list(map(int, input().split()))
	maxi = max(s)
	c = s.copy()
	ind = s.index(maxi)
	c.pop(ind)
	maxim = max(c)
	pr = []
	for i in s:
		if i != maxi:
			pr.append(i - maxi)
		else:
			pr.append(i - maxim)
	if x != t - 1:
		print(' '.join((str(i) for i in pr)), end=' \n')
	else:
		print(' '.join((str(i) for i in pr)))
pass


def solve():
	(mx, s_mx) = (0, 0)
	n = int(input())
	l = list(map(int, input().split()))
	for num in l:
		if num >= mx:
			(mx, s_mx) = (num, mx)
		elif num >= s_mx:
			s_mx = num
	for num in l:
		if num == mx:
			print(num - s_mx, end=' ')
		else:
			print(num - mx, end=' ')
	print()
t = int(input())
for _ in range(t):
	solve()


def read():
	return list(map(int, input().split()))

def task():
	n = int(input())
	a = read()
	best = max(a)
	best_i = a.index(best)
	next_best = max(a[0:best_i] + a[best_i + 1:])
	for i in range(n):
		if i == best_i:
			print(-next_best + a[i], end=' ')
			continue
		print(-best + a[i], end=' ')
	print()
t = int(input())
for i in range(t):
	task()


n = int(input())
for i in range(n):
	arr = int(input())
	l = list(map(int, input().split()))
	ll = l.copy()
	maxx = max(l)
	l.remove(maxx)
	second = max(l)
	for i in ll:
		if i == maxx:
			print(maxx - second, end=' ')
		else:
			print(i - maxx, end=' ')
	print()


w = int(input())
for roma in range(w):
	a = int(input())
	q = list(map(int, input().split()))
	mx = max(q)
	q[q.index(mx)] = 0
	mx2 = max(q)
	q[q.index(0)] = mx
	for i in q:
		if i != mx:
			print(i - mx, end=' ')
		else:
			print(mx - mx2, end=' ')
	print()


def main(s):
	(first, second) = (-1, -1)
	for ss in s:
		if ss >= first:
			second = first
			first = ss
		elif ss >= second:
			second = ss
	for x in s:
		if x == first:
			print(x - second, end=' ')
		else:
			print(x - first, end=' ')
	print()
t = int(input())
for i in range(t):
	n = int(input())
	s = list(map(int, input().split()))
	main(s)


def solve(n, l):
	max_1 = max(l[0], l[1])
	max_2 = min(l[0], l[1])
	for i in range(2, n):
		if l[i] > max_1:
			max_2 = max_1
			max_1 = l[i]
		elif l[i] > max_2:
			max_2 = l[i]
	for i in l:
		if i == max_1:
			print(i - max_2, end=' ')
		else:
			print(i - max_1, end=' ')
	print()
for i in range(int(input())):
	n = int(input())
	l = list(map(int, input().split()))
	solve(n, l)


import sys
input = sys.stdin.readline

def solution():
	T = int(input())
	for t in range(T):
		N = int(input())
		num = list(map(int, input().split()))
		(first, second) = (0, 0)
		for i in num:
			if i >= first:
				second = first
				first = i
			elif i >= second:
				second = i
		for i in range(N):
			if num[i] == first:
				num[i] -= second
			else:
				num[i] -= first
		for i in num:
			print(i, end=' ')
		print()
solution()


t = int(input())
for i in range(0, t):
	n = int(input())
	s = list(map(int, input().split()))
	temp = s.copy()
	a = max(temp)
	temp.remove(a)
	b = max(temp)
	for i in range(0, n):
		if s[i] == a:
			print(a - b, end=' ')
		else:
			print(s[i] - a, end=' ')
	print()


t = int(input())
for _ in range(t):
	n = int(input())
	s = list(map(int, input().split()))
	sil_max = max(s)
	silac = s.index(sil_max)
	for i in range(n):
		if i == silac:
			print(sil_max - max(s[0:silac] + s[silac + 1:]), end=' ')
		else:
			print(s[i] - sil_max, end=' ')
	print()