human
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.
Solve the task in PYTHON3.

=====
Give me a Python code to determine if Petya can sort his array a, i?
assistant
#Here is Python code to determine if Petya can sort his array a, i.

import io,os
input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

class fenwick(object):
    def __init__(self, n):
        self.n = n
        self.cul = [0]*n

    def update(self,index,diff):
        i = index
        while i<self.n:
            self.cul[i] += diff
            i += (i+1)&(-i-1)

    def getaccu(self,index):
        output = 0
        i = index
        while i>=0:
            output += self.cul[i]
            i -= (i+1)&(-i-1)
        return output


def main(t):

    n = int(input())
    arr = list(map(int,input().split()))

    dic = {}
    for num in arr:
        if num not in dic:  dic[num] = 1
        else:  
            print("YES")
            return 


    
    fen = fenwick(n+2)
    ans = 0
    for num in arr[::-1]:
        ans += fen.getaccu(num-1)
        fen.update(num,1)


#    print(ans)

    if ans%2==1:  print("NO")
    else:  print("YES")
    

        















T = int(input())
t = 1
while t<=T:
    main(t)
    t += 1