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: 
  class SegmentTree():
      def __init__(self,arr,combinerFunction,isCommutative=True): # isCommutative means f(a,b)==f(b,a)
          self.n=len(arr)
          def cmb(a,b):
              if a==None: return b
              if b==None: return a
              return combinerFunction(a,b)
          self.cmb=cmb
          self.sz=self.n if isCommutative else pow(2,((self.n-1).bit_length())) # non-commutative needs power of 2 size
          self.t=[None]*(2*self.sz) # use None as initial value
          for i in range(self.n): self.t[i+self.sz]=arr[i]
          for i in range(self.sz-1,0,-1): self.pull(i)
      def pull(self,p):
          self.t[p]=self.cmb(self.t[2*p],self.t[2*p+1])
      def update(self,idx,val): # set val at idx
          idx+=self.sz
          self.t[idx]=val
          idx//=2
          while idx>0:
              self.pull(idx)
              idx//=2
      def query(self,l,r): # aggregated value in [l,r] inclusive
          l+=self.sz; r+=self.sz+1
          a=b=None
          while l<r:
              if l%2==1: a=self.cmb(a,self.t[l]); l+=1
              if r%2==1: r-=1; b=self.cmb(self.t[r],b)
              l//=2; r//=2
          return self.cmb(a,b)
  def getMaxSegTree(arr):
      return SegmentTree(arr,lambda a,b:max(a,b),True)
  def getMinSegTree(arr):
      return SegmentTree(arr,lambda a,b:min(a,b),True)
  def getSumSegTree(arr):
      return SegmentTree(arr,lambda a,b:a+b,True)
  
  def main():
      
      t = int(input())
      allans = []
      for _ in range(t):
          n = int(input())
          a = readIntArr()
          if len(set(a)) < n: # at least 1 repeated element
              allans.append('YES')
          else:
              # coord-compress
              b = sorted(a)
              mapp = {x : i for i, x in enumerate(b)}
              for i in range(n):
                  a[i] = mapp[a[i]]
              # count inversions
              seggy = getSumSegTree([0] * n)
              invCnts = 0
              for x in a:
                  if x < n - 1:
                      invCnts += seggy.query(x + 1, n - 1)
                  seggy.update(x, 1)
              
              # since a 3-cycle is equivalent to 2 swaps, invCnts must be even
              if invCnts % 2 == 0:
                  allans.append('YES')
              else:
                  allans.append('NO')
              
      multiLineArrayPrint(allans)
      
      return
  
  
  import sys
  input=sys.stdin.buffer.readline #FOR READING PURE INTEGER INPUTS (space separation ok)
  # input=lambda: sys.stdin.readline().rstrip("\r\n") #FOR READING STRING/TEXT INPUTS.
  
  def oneLineArrayPrint(arr):
      print(' '.join([str(x) for x in arr]))
  def multiLineArrayPrint(arr):
      print('\n'.join([str(x) for x in arr]))
  def multiLineArrayOfArraysPrint(arr):
      print('\n'.join([' '.join([str(x) for x in y]) for y in arr]))
   
  def readIntArr():
      return [int(x) for x in input().split()]
  # def readFloatArr():
  #     return [float(x) for x in input().split()]
   
  def makeArr(defaultValFactory,dimensionArr): # eg. makeArr(lambda:0,[n,m])
      dv=defaultValFactory;da=dimensionArr
      if len(da)==1:return [dv() for _ in range(da[0])]
      else:return [makeArr(dv,da[1:]) for _ in range(da[0])]
   
  def queryInteractive(i,j):
      print('? {} {}'.format(i,j))
      sys.stdout.flush()
      return int(input())
   
  def answerInteractive(i,j,k):
      print('! {} {} {}'.format(i,j,k))
      sys.stdout.flush()
   
  inf=float('inf')
  # MOD=10**9+7
  # MOD=998244353
  
  from math import gcd,floor,ceil
  import math
  # from math import floor,ceil # for Python2
   
  for _abc in range(1):
      main()