#include <bits/stdc++.h>
using namespace std;
const long long M = 1e9 + 7;
const int N = 2e5 + 5;
long long power(long long x, long long y, long long p) {
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long mi(long long x) { return power(x, M - 2, M); }
int nCr(int n, int r) {
  int mod = 1000000007;
  int C[r + 1];
  memset(C, 0, sizeof(C));
  C[0] = 1;
  for (int i = 1; i <= n; i++) {
    for (int j = min(i, r); j > 0; j--) {
      C[j] = (C[j] + C[j - 1]) % mod;
    }
  }
  return C[r] % mod;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long T;
  cin >> T;
  while (T--) {
    long long n;
    cin >> n;
    vector<long long> v(n);
    long long fg = 0;
    map<long long, long long> mp;
    vector<long long> v2;
    for (long long i = 0; i < n; i++) {
      cin >> v[i];
      if (mp[v[i]] != 0) {
        fg = 1;
      }
      mp[v[i]]++;
      v2.push_back(v[i]);
    }
    if (fg) {
      cout << "YES" << endl;
    } else {
      sort(v2.begin(), v2.end());
      map<long long, long long> m;
      for (long long i = 0; i < n; i++) {
        m[v2[i]] = i;
      }
      vector<long long> vis(n, 0);
      long long cn1 = 0, cn2 = 0;
      for (long long i = 0; i < n; i++) {
        if (m[v[i]] == i) {
          continue;
        }
        if (!vis[i]) {
          vis[i] = 1;
          long long pres = i;
          long long st = m[v[i]];
          long long cn = 1;
          while (st != pres) {
            vis[st] = 1;
            cn++;
            st = m[v[st]];
          }
          if (cn % 2 != 0) {
            cn1++;
          } else {
            cn2++;
          }
        }
      }
      if (cn2 % 2 == 0) {
        cout << "YES" << endl;
      } else {
        cout << "NO" << endl;
      }
    }
  }
  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;
const long long M = 1e9 + 7;
const int N = 2e5 + 5;
long long power(long long x, long long y, long long p) {
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long mi(long long x) { return power(x, M - 2, M); }
int nCr(int n, int r) {
  int mod = 1000000007;
  int C[r + 1];
  memset(C, 0, sizeof(C));
  C[0] = 1;
  for (int i = 1; i <= n; i++) {
    for (int j = min(i, r); j > 0; j--) {
      C[j] = (C[j] + C[j - 1]) % mod;
    }
  }
  return C[r] % mod;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long T;
  cin >> T;
  while (T--) {
    long long n;
    cin >> n;
    vector<long long> v(n);
    long long fg = 0;
    map<long long, long long> mp;
    vector<long long> v2;
    for (long long i = 0; i < n; i++) {
      cin >> v[i];
      if (mp[v[i]] != 0) {
        fg = 1;
      }
      mp[v[i]]++;
      v2.push_back(v[i]);
    }
    if (fg) {
      cout << "YES" << endl;
    } else {
      sort(v2.begin(), v2.end());
      map<long long, long long> m;
      for (long long i = 0; i < n; i++) {
        m[v2[i]] = i;
      }
      vector<long long> vis(n, 0);
      long long cn1 = 0, cn2 = 0;
      for (long long i = 0; i < n; i++) {
        if (m[v[i]] == i) {
          continue;
        }
        if (!vis[i]) {
          vis[i] = 1;
          long long pres = i;
          long long st = m[v[i]];
          long long cn = 1;
          while (st != pres) {
            vis[st] = 1;
            cn++;
            st = m[v[st]];
          }
          if (cn % 2 != 0) {
            cn1++;
          } else {
            cn2++;
          }
        }
      }
      if (cn2 % 2 == 0) {
        cout << "YES" << endl;
      } else {
        cout << "NO" << endl;
      }
    }
  }
  return 0;
}

```