#include <bits/stdc++.h>
const long long MAXN = 500005;
long long bit[MAXN];
void add(long long x, long long v) {
  x += 1;
  while (x < MAXN) {
    bit[x] += v;
    x += x & (-x);
  }
}
long long sum(long long x) {
  x += 1;
  long long ret = 0;
  while (x > 0) {
    ret += bit[x];
    x -= x & (-x);
  }
  return ret;
}
signed main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  long long t;
  std::cin >> t;
  while (t--) {
    long long n;
    std::cin >> n;
    for (long long i = 0; i <= n; i++) bit[i] = 0;
    std::pair<long long, long long> help[n];
    for (long long i = 0; i < n; i++) {
      std::cin >> help[i].first;
      help[i].second = i;
    }
    if (n < 3) {
      bool sorted = true;
      for (long long i = 0; i + 1 < n; i++) {
        if (help[i] > help[i + 1]) sorted = false;
      }
      std::cout << (sorted ? "YES" : "NO") << std::endl;
      continue;
    }
    std::set<long long> set;
    long long done = 0;
    for (long long i = 0; i < n; i++) {
      if (set.count(help[i].first)) done = 1;
      set.insert(help[i].first);
    }
    if (done) {
      std::cout << "YES" << std::endl;
      continue;
    }
    std::sort(help, help + n);
    long long cur = 0;
    for (long long i = n - 1; i >= 0; i--) {
      cur += sum(help[i].second);
      add(help[i].second, 1);
    }
    std::cout << (cur % 2 == 0 ? "YES" : "NO") << std::endl;
  }
  return 0;
}

### Prompt

In Cpp, your task is to solve 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>
const long long MAXN = 500005;
long long bit[MAXN];
void add(long long x, long long v) {
  x += 1;
  while (x < MAXN) {
    bit[x] += v;
    x += x & (-x);
  }
}
long long sum(long long x) {
  x += 1;
  long long ret = 0;
  while (x > 0) {
    ret += bit[x];
    x -= x & (-x);
  }
  return ret;
}
signed main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);
  long long t;
  std::cin >> t;
  while (t--) {
    long long n;
    std::cin >> n;
    for (long long i = 0; i <= n; i++) bit[i] = 0;
    std::pair<long long, long long> help[n];
    for (long long i = 0; i < n; i++) {
      std::cin >> help[i].first;
      help[i].second = i;
    }
    if (n < 3) {
      bool sorted = true;
      for (long long i = 0; i + 1 < n; i++) {
        if (help[i] > help[i + 1]) sorted = false;
      }
      std::cout << (sorted ? "YES" : "NO") << std::endl;
      continue;
    }
    std::set<long long> set;
    long long done = 0;
    for (long long i = 0; i < n; i++) {
      if (set.count(help[i].first)) done = 1;
      set.insert(help[i].first);
    }
    if (done) {
      std::cout << "YES" << std::endl;
      continue;
    }
    std::sort(help, help + n);
    long long cur = 0;
    for (long long i = n - 1; i >= 0; i--) {
      cur += sum(help[i].second);
      add(help[i].second, 1);
    }
    std::cout << (cur % 2 == 0 ? "YES" : "NO") << std::endl;
  }
  return 0;
}

```