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,os,io
  input = sys.stdin.readline # for strings
  # input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline # for non-strings
  
  PI = 3.141592653589793238460
  INF =  float('inf')
  MOD  = 1000000007
  # MOD = 998244353
  
  
  def bin32(num):
      return '{0:032b}'.format(num)
  
  def add(x,y):
      return (x+y)%MOD
  
  def sub(x,y):
      return (x-y+MOD)%MOD
  
  def mul(x,y):
      return (x*y)%MOD
  
  def gcd(x,y):
      if y == 0:
          return x
      return gcd(y,x%y)
  
  def lcm(x,y):
      return (x*y)//gcd(x,y)
  
  def power(x,y):
      res = 1
      x%=MOD
      while y!=0:
          if y&1 :
              res = mul(res,x)
          y>>=1
          x = mul(x,x)
          
      return res
          
  def mod_inv(n):
      return power(n,MOD-2)
  
  def prob(p,q):
      return mul(p,power(q,MOD-2))    
    
  def ii():
      return int(input())
  
  def li():
      return [int(i) for i in input().split()]
  
  def ls():
      return [i for i in input().split()]
  
  for t in range(ii()):
      t+=1
      n = ii()
      a = li()
  
      if n == 1:
          print('YES')
          continue
      if n == 2:
          if sorted(a) == a:
              print("YES")
          else:
              print("NO")
          continue
      se = set()
      for  i in a:
          se.add(i)
      if len(se) != n:
          print("YES")
          continue
      
      ind = [-1 for i in range(n+1)]
      a.insert(0 , 0)
      for i in range(1,n+1):
          ind[a[i]] = i
      
      i = 1
      # print(a,a)
      while i <= n :
          if a[i] == i:
              i+=1
              continue
          
          # 3 .... 1  ... 2
          x = i
          y = ind[i]
          z = a[i]
          # print(t , x ,y , z,a)
          if y == z:
              z = i + 1
          if y == z:
              z = i + 2
          if z > n:
              break
          # print(x , y ,z)
          a[x] , a[y] , a[z] = a[y] , a[z] , a[x]
          ind[a[x]] = x
          ind[a[y]] = y
          ind[a[z]] = z
          i+=1
      
      if a == sorted(a):
          print("YES")
      else:
          print("NO")