description: Petya has an array of integers a_1, a_2, …, a_n. He only likes sorted arrays. Unfortunately, the given array could be arbitrary, so Petya wants to sort it.
  
  Petya likes to challenge himself, so he wants to sort array using only 3-cycles. More formally, in one operation he can pick 3 pairwise distinct indices i, j, and k (1 ≤ i, j, k ≤ n) and apply i → j → k → i cycle to the array a. It simultaneously places a_i on position j, a_j on position k, and a_k on position i, without changing any other element.
  
  For example, if a is [10, 50, 20, 30, 40, 60] and he chooses i = 2, j = 1, k = 5, then the array becomes [\underline{50}, \underline{40}, 20, 30, \underline{10}, 60].
  
  Petya can apply arbitrary number of 3-cycles (possibly, zero). You are to determine if Petya can sort his array a, i. e. make it non-decreasing.
  
  Input
  
  Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 5 ⋅ 10^5). Description of the test cases follows.
  
  The first line of each test case contains a single integer n (1 ≤ n ≤ 5 ⋅ 10^5) — the length of the array a.
  
  The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ n).
  
  It is guaranteed that the sum of n over all test cases does not exceed 5 ⋅ 10^5.
  
  Output
  
  For each test case, print "YES" (without quotes) if Petya can sort the array a using 3-cycles, and "NO" (without quotes) otherwise. You can print each letter in any case (upper or lower).
  
  Example
  
  Input
  
  
  7
  1
  1
  2
  2 2
  2
  2 1
  3
  1 2 3
  3
  2 1 3
  3
  3 1 2
  4
  2 1 4 3
  
  
  Output
  
  
  YES
  YES
  NO
  YES
  NO
  YES
  YES
  
  Note
  
  In the 6-th test case Petya can use the 3-cycle 1 → 3 → 2 → 1 to sort the array.
  
  In the 7-th test case Petya can apply 1 → 3 → 2 → 1 and make a = [1, 4, 2, 3]. Then he can apply 2 → 4 → 3 → 2 and finally sort the array.
solution: 
  import sys
  from sys import stdin
  
  """
  N = 4
  s = set()
  tp = tuple([i for i in range(N)])
  s.add( tp )
  
  q = [tp]
  
  
  
  while q:
      v = q[-1]
      del q[-1]
  
      for i in range(N):
          for j in range(N):
              for k in range(N):
  
                  if len(set([i,j,k])) != 3:
                      continue
  
                  l = list(v)
                  #print (l)
                  l[i],l[j],l[k] = l[j],l[k],l[i]
                  t = tuple(l)
  
                  if t not in s:
                      s.add(t)
                      q.append(t)
  
  print (s)
  """
  
  def bitadd(a,w,bit): 
   
      x = a
      while x <= (len(bit)-1):
          bit[x] += w
          x += x & (-1 * x)
   
  def bitsum(a,bit): 
   
      ret = 0
      x = a
      while x > 0:
          ret += bit[x]
          x -= x & (-1 * x)
      return ret
  
  
  
  
  
  
  
  tt = int(stdin.readline())
  
  ANS = []
  for loop in range(tt):
  
      N = n = int(stdin.readline())
      a = list(map(int,stdin.readline().split()))
  
      dic = {}
      lis = []
      for i in range(n):
          if a[i] not in dic:
              dic[a[i]] = 0
              lis.append(a[i])
      lis.sort()
      for i in range(len(lis)):
          dic[lis[i]] = i+1
          
      if len(dic) != n:
          ANS.append("YES")
          continue
  
      BIT = [0] * (len(lis)+2)
  
      ans = 0
      for i in range(N):
  
          ans += i - bitsum(dic[a[i]],BIT)
          bitadd(dic[a[i]],1,BIT)
  
      if ans % 2 == 0:
          ANS.append("YES")
      else:
          ANS.append("NO")
  
  print ("\n".join(ANS))
      