#include <bits/stdc++.h>
using namespace std;
long long ans = 0, A[500000];
int partition(long long arr[], int low, int high) {
  int r = low + rand() % (high - low + 1);
  if (r != high) {
    swap(arr[r], arr[high]);
    ans++;
  }
  int pivot = arr[high];
  int i = (low - 1);
  for (int j = low; j <= high - 1; j++) {
    if (arr[j] < pivot) {
      i++;
      swap(arr[i], arr[j]);
      if (i != j) ans++;
    }
  }
  swap(arr[i + 1], arr[high]);
  if (i + 1 != high) ans++;
  return (i + 1);
}
void quickSort(long long arr[], int low, int high) {
  if (low < high) {
    int pi = partition(arr, low, high);
    quickSort(arr, low, pi - 1);
    quickSort(arr, pi + 1, high);
  }
}
int main() {
  long long T, i, j, n, m, k;
  cin >> T;
  while (T--) {
    cin >> n;
    for (i = 0; i < n; ++i) {
      cin >> A[i];
    }
    ans = 0;
    quickSort(A, 0, n - 1);
    for (i = 1; i < n; ++i)
      if (A[i] == A[i - 1]) break;
    if (i < n)
      cout << "YES\n";
    else if (ans % 2)
      cout << "NO\n";
    else
      cout << "YES\n";
  }
}

### Prompt

Your challenge is to write a Cpp solution to the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
long long ans = 0, A[500000];
int partition(long long arr[], int low, int high) {
  int r = low + rand() % (high - low + 1);
  if (r != high) {
    swap(arr[r], arr[high]);
    ans++;
  }
  int pivot = arr[high];
  int i = (low - 1);
  for (int j = low; j <= high - 1; j++) {
    if (arr[j] < pivot) {
      i++;
      swap(arr[i], arr[j]);
      if (i != j) ans++;
    }
  }
  swap(arr[i + 1], arr[high]);
  if (i + 1 != high) ans++;
  return (i + 1);
}
void quickSort(long long arr[], int low, int high) {
  if (low < high) {
    int pi = partition(arr, low, high);
    quickSort(arr, low, pi - 1);
    quickSort(arr, pi + 1, high);
  }
}
int main() {
  long long T, i, j, n, m, k;
  cin >> T;
  while (T--) {
    cin >> n;
    for (i = 0; i < n; ++i) {
      cin >> A[i];
    }
    ans = 0;
    quickSort(A, 0, n - 1);
    for (i = 1; i < n; ++i)
      if (A[i] == A[i - 1]) break;
    if (i < n)
      cout << "YES\n";
    else if (ans % 2)
      cout << "NO\n";
    else
      cout << "YES\n";
  }
}

```