#include <bits/stdc++.h>
using namespace std;
int main() {
  int T;
  cin >> T;
  while (T--) {
    int N;
    cin >> N;
    int A[N];
    map<int, set<int> > M;
    bool res = false;
    for (int i = 0; i < N; i++) {
      cin >> A[i];
      M[A[i]].insert(i);
      if (M[A[i]].size() > 1) {
        res = true;
      }
    }
    if (res) {
      cout << "YES\n";
      continue;
    }
    for (int i = N - 1; i >= 2; i--) {
      auto itr = M.rbegin();
      int ele = (*itr).first;
      if (ele == A[i]) {
        if ((*itr).second.size() == 1) {
          M.erase(ele);
        } else {
          (*itr).second.erase(i);
        }
        continue;
      }
      int i1, i2, i3;
      auto itr2 = (*itr).second.begin();
      if ((*itr2) == 0) {
        i1 = 0;
        i2 = 1;
        i3 = i;
        int x = A[i1], y = A[i2], z = A[i3];
        if (M[x].size() == 1) {
          M.erase(x);
        } else {
          M[x].erase(i1);
        }
        M[z].insert(i2);
        M[z].erase(i3);
        M[y].erase(i2);
        M[y].insert(i1);
        swap(A[i2], A[i3]);
        swap(A[i1], A[i3]);
      } else {
        i1 = 0;
        i2 = *((*itr).second.begin());
        i3 = i;
        int x = A[i1], y = A[i2], z = A[i3];
        M[z].erase(i3);
        M[z].insert(i1);
        M[x].insert(i2);
        M[x].erase(i1);
        if (M[y].size() == 1) {
          M.erase(y);
        } else {
          M[y].erase(i2);
        }
        swap(A[i2], A[i3]);
        swap(A[i1], A[i2]);
      }
    }
    if (A[0] <= A[1]) {
      cout << "YES\n";
    } else {
      cout << "NO\n";
    }
  }
  return 0;
}

### Prompt

Please create a solution in CPP 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;
int main() {
  int T;
  cin >> T;
  while (T--) {
    int N;
    cin >> N;
    int A[N];
    map<int, set<int> > M;
    bool res = false;
    for (int i = 0; i < N; i++) {
      cin >> A[i];
      M[A[i]].insert(i);
      if (M[A[i]].size() > 1) {
        res = true;
      }
    }
    if (res) {
      cout << "YES\n";
      continue;
    }
    for (int i = N - 1; i >= 2; i--) {
      auto itr = M.rbegin();
      int ele = (*itr).first;
      if (ele == A[i]) {
        if ((*itr).second.size() == 1) {
          M.erase(ele);
        } else {
          (*itr).second.erase(i);
        }
        continue;
      }
      int i1, i2, i3;
      auto itr2 = (*itr).second.begin();
      if ((*itr2) == 0) {
        i1 = 0;
        i2 = 1;
        i3 = i;
        int x = A[i1], y = A[i2], z = A[i3];
        if (M[x].size() == 1) {
          M.erase(x);
        } else {
          M[x].erase(i1);
        }
        M[z].insert(i2);
        M[z].erase(i3);
        M[y].erase(i2);
        M[y].insert(i1);
        swap(A[i2], A[i3]);
        swap(A[i1], A[i3]);
      } else {
        i1 = 0;
        i2 = *((*itr).second.begin());
        i3 = i;
        int x = A[i1], y = A[i2], z = A[i3];
        M[z].erase(i3);
        M[z].insert(i1);
        M[x].insert(i2);
        M[x].erase(i1);
        if (M[y].size() == 1) {
          M.erase(y);
        } else {
          M[y].erase(i2);
        }
        swap(A[i2], A[i3]);
        swap(A[i1], A[i2]);
      }
    }
    if (A[0] <= A[1]) {
      cout << "YES\n";
    } else {
      cout << "NO\n";
    }
  }
  return 0;
}

```