description: Vupsen and Pupsen were gifted an integer array. Since Vupsen doesn't like the number 0, he threw away all numbers equal to 0 from the array. As a result, he got an array a of length n.
  
  Pupsen, on the contrary, likes the number 0 and he got upset when he saw the array without zeroes. To cheer Pupsen up, Vupsen decided to come up with another array b of length n such that ∑_{i=1}^{n}a_i ⋅ b_i=0. Since Vupsen doesn't like number 0, the array b must not contain numbers equal to 0. Also, the numbers in that array must not be huge, so the sum of their absolute values cannot exceed 10^9. Please help Vupsen to find any such array b!
  
  Input
  
  The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases. The next 2 ⋅ t lines contain the description of test cases. The description of each test case consists of two lines.
  
  The first line of each test case contains a single integer n (2 ≤ n ≤ 10^5) — the length of the array.
  
  The second line contains n integers a_1, a_2, …, a_n (-10^4 ≤ a_i ≤ 10^4, a_i ≠ 0) — the elements of the array a.
  
  It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.
  
  Output
  
  For each test case print n integers b_1, b_2, …, b_n — elements of the array b (|b_1|+|b_2|+… +|b_n| ≤ 10^9, b_i ≠ 0, ∑_{i=1}^{n}a_i ⋅ b_i=0).
  
  It can be shown that the answer always exists.
  
  Example
  
  Input
  
  
  3
  2
  5 5
  5
  5 -2 10 -9 4
  7
  1 2 3 4 5 6 7
  
  
  Output
  
  
  1 -1
  -1 5 1 -1 -1
  -10 2 2 -3 5 -1 -1
  
  Note
  
  In the first test case, 5 ⋅ 1 + 5 ⋅ (-1)=5-5=0. You could also print 3 -3, for example, since 5 ⋅ 3 + 5 ⋅ (-3)=15-15=0
  
  In the second test case, 5 ⋅ (-1) + (-2) ⋅ 5 + 10 ⋅ 1 + (-9) ⋅ (-1) + 4 ⋅ (-1)=-5-10+10+9-4=0.
solution: import sys
  import math
  import random
  import collections
  
  def solve(a, b, c):
      if c == 0:
          return 0, 0
      if a > b:
          x, y = solve(b, a, c)
          return y, x
      if c % a == 0:
          return c // a, 0
      if c % b == 0:
          return 0, c // b
      if c >= a:
          x, y = solve(a, b, c % a)
          return x + c // a, y
      x, y = solve(b % a, a, c)
      return y - (b // a) * x, x
  
  T = int(sys.stdin.readline().strip())
  
  for _ in range(T):
      n = int(sys.stdin.readline().strip())
      a = list(map(int, sys.stdin.readline().strip().split(" ")))
      cnt = collections.Counter(a)
      if len(cnt) == 1:
          res = [1] * n
          res[0] = -n + 1
          print(' '.join(map(str, res)))
          continue
      if len(cnt) == 2:
          x, y = list(cnt.keys())
          if x == -y:
              res = [1] * n
              res[0] = -(sum(a) // a[0]) + 1
              while res[0] == 0 or res[1] == 0:
                  if a[0] == a[1]:
                      res[0] += 1
                      res[1] -= 1
                  else:
                      res[0] += 1
                      res[1] += 1
              print(' '.join(map(str, res)))
              continue
      if n == 2:
          x, y = a
          g = math.gcd(x, y)
          print(y // g, -x // g)
          continue
      keys = list(cnt.keys())
      p = random.choice(keys)
      q = random.choice(keys)
      while abs(p) == abs(q):
          q = random.choice(keys)
      for i in range(n):
          if a[i] == p:
              p = i
              break
      for i in range(n):
          if a[i] == q:
              q = i
              break
      s = 0
      res = [0] * n
      g = math.gcd(abs(a[p]), abs(a[q]))
      for i in range(n):
          if i == p or i == q:
              continue
          if a[i] <= 0 and s <= 0:
              res[i] = -g
              s -= a[i] * g
          elif a[i] <= 0 <= s:
              res[i] = g
              s += a[i] * g
          elif s <= 0 <= a[i]:
              res[i] = g
              s += a[i] * g
          elif a[i] >= 0 and s >= 0:
              res[i] = -g
              s -= a[i] * g
      target = -s
      # x * a[p] + y * a[q] = target
      # solve x, y
      aa = abs(a[p])
      bb = abs(a[q])
      gap = math.gcd(aa, bb)
      aa //= gap
      bb //= gap
      cc = abs(target) // gap
      x, y = solve(aa, bb, cc)
      while x == 0 or y == 0:
          x += bb
          y += -aa
      flag = 0
      for i in {-1, 1}:
          for j in {-1, 1}:
              if a[p] * x * i + a[q] * y * j == target:
                  res[p] = x * i
                  res[q] = y * j
                  flag = 1
                  break
          if flag:
              break
      print(' '.join(map(str, res)))
      # print(sum([s * t for s, t in zip(a, res)]) == 0)
      
  