#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = double;
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<ld, ld>;
using cd = complex<ld>;
using vcd = vector<cd>;
using vi = vector<int>;
using vl = vector<ll>;
using vd = vector<ld>;
using vs = vector<string>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
template <class T>
using min_pq = priority_queue<T, vector<T>, greater<T> >;
template <class T>
inline int ckmin(T& a, const T& val) {
  return val < a ? a = val, 1 : 0;
}
template <class T>
inline int ckmax(T& a, const T& val) {
  return a < val ? a = val, 1 : 0;
}
template <class T>
void remDup(vector<T>& v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), end(v));
}
constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int bits(int x) { return x == 0 ? 0 : 31 - __builtin_clz(x); }
constexpr int p2(int x) { return 1 << x; }
constexpr int msk2(int x) { return p2(x) - 1; }
ll ceilDiv(ll a, ll b) { return a / b + ((a ^ b) > 0 && a % b); }
ll floorDiv(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); }
void setPrec(int x) { cout << fixed << setprecision(x); }
string to_string(char c) { return string(1, c); }
string to_string(const char* s) { return (string)s; }
string to_string(string s) { return s; }
string to_string(bool b) { return to_string((int)b); }
template <class T>
string to_string(complex<T> c) {
  stringstream ss;
  ss << c;
  return ss.str();
}
template <class T>
using V = vector<T>;
string to_string(V<bool> v) {
  string res = "{";
  for (int i = (0); i <= (int((v).size()) - 1); i++) res += char('0' + v[i]);
  res += "}";
  return res;
}
template <size_t sz>
string to_string(bitset<sz> b) {
  string res = "";
  for (int i = (0); i <= (int((b).size()) - 1); i++) res += char('0' + b[i]);
  return res;
}
template <class T, class U>
string to_string(pair<T, U> p);
template <class T>
string to_string(T v) {
  bool fst = 1;
  string res = "";
  for (const auto& x : v) {
    if (!fst) res += " ";
    fst = 0;
    res += to_string(x);
  }
  return res;
}
template <class T, class U>
string to_string(pair<T, U> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <class T>
void pr(T x) {
  cout << to_string(x);
}
template <class T, class... U>
void pr(const T& t, const U&... u) {
  pr(t);
  pr(u...);
}
void ps() { pr("\n"); }
template <class T, class... U>
void ps(const T& t, const U&... u) {
  pr(t);
  if (sizeof...(u)) pr(" ");
  ps(u...);
}
void DBG() { cerr << "]" << endl; }
template <class T, class... U>
void DBG(const T& t, const U&... u) {
  cerr << to_string(t);
  if (sizeof...(u)) cerr << ", ";
  DBG(u...);
}
const ld PI = acos(-1.0);
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const ld EPS = 1e-9;
const ll MODBASE = 1000000007LL;
const int INF = 0x3f3f3f3f;
const int MAXN = 500010;
const int MAXM = 1000;
const int MAXK = 16;
const int MAXQ = 200010;
int n, a[MAXN], b[MAXN], c[MAXN];
struct BinaryIndexedTree {
 public:
  BinaryIndexedTree(int n) {
    N = n;
    t.resize(N + 1);
    for (int i = (0); i <= (N); i++) t[i] = 0;
  }
  void update(int u, int val) {
    while (u <= N) {
      t[u] += val;
      u = u + (u & (-u));
    }
  }
  ll get(int u) {
    ll res = 0;
    while (u) {
      res += t[u];
      u = u - (u & (-u));
    }
    return res;
  }

 private:
  vector<ll> t;
  int N;
};
bool check() {
  for (int i = (1); i <= (n); i++) c[i] = 0;
  for (int i = (1); i <= (n); i++) {
    if (c[a[i]] == 0)
      c[a[i]] = 1;
    else
      return 1;
  }
  BinaryIndexedTree bit(n);
  ll sum = 0;
  for (int i = (n); i >= (1); i--) {
    sum += bit.get(a[i]);
    bit.update(a[i], 1);
  }
  return sum % 2 == 0;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(nullptr);
  int te;
  cin >> te;
  while (te--) {
    cin >> n;
    for (int i = (1); i <= (n); i++) cin >> a[i];
    if (check())
      cout << "YES"
           << "\n";
    else
      cout << "NO\n";
  }
  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>
using namespace std;
using ll = long long;
using ld = double;
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<ld, ld>;
using cd = complex<ld>;
using vcd = vector<cd>;
using vi = vector<int>;
using vl = vector<ll>;
using vd = vector<ld>;
using vs = vector<string>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
template <class T>
using min_pq = priority_queue<T, vector<T>, greater<T> >;
template <class T>
inline int ckmin(T& a, const T& val) {
  return val < a ? a = val, 1 : 0;
}
template <class T>
inline int ckmax(T& a, const T& val) {
  return a < val ? a = val, 1 : 0;
}
template <class T>
void remDup(vector<T>& v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), end(v));
}
constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int bits(int x) { return x == 0 ? 0 : 31 - __builtin_clz(x); }
constexpr int p2(int x) { return 1 << x; }
constexpr int msk2(int x) { return p2(x) - 1; }
ll ceilDiv(ll a, ll b) { return a / b + ((a ^ b) > 0 && a % b); }
ll floorDiv(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); }
void setPrec(int x) { cout << fixed << setprecision(x); }
string to_string(char c) { return string(1, c); }
string to_string(const char* s) { return (string)s; }
string to_string(string s) { return s; }
string to_string(bool b) { return to_string((int)b); }
template <class T>
string to_string(complex<T> c) {
  stringstream ss;
  ss << c;
  return ss.str();
}
template <class T>
using V = vector<T>;
string to_string(V<bool> v) {
  string res = "{";
  for (int i = (0); i <= (int((v).size()) - 1); i++) res += char('0' + v[i]);
  res += "}";
  return res;
}
template <size_t sz>
string to_string(bitset<sz> b) {
  string res = "";
  for (int i = (0); i <= (int((b).size()) - 1); i++) res += char('0' + b[i]);
  return res;
}
template <class T, class U>
string to_string(pair<T, U> p);
template <class T>
string to_string(T v) {
  bool fst = 1;
  string res = "";
  for (const auto& x : v) {
    if (!fst) res += " ";
    fst = 0;
    res += to_string(x);
  }
  return res;
}
template <class T, class U>
string to_string(pair<T, U> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <class T>
void pr(T x) {
  cout << to_string(x);
}
template <class T, class... U>
void pr(const T& t, const U&... u) {
  pr(t);
  pr(u...);
}
void ps() { pr("\n"); }
template <class T, class... U>
void ps(const T& t, const U&... u) {
  pr(t);
  if (sizeof...(u)) pr(" ");
  ps(u...);
}
void DBG() { cerr << "]" << endl; }
template <class T, class... U>
void DBG(const T& t, const U&... u) {
  cerr << to_string(t);
  if (sizeof...(u)) cerr << ", ";
  DBG(u...);
}
const ld PI = acos(-1.0);
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const ld EPS = 1e-9;
const ll MODBASE = 1000000007LL;
const int INF = 0x3f3f3f3f;
const int MAXN = 500010;
const int MAXM = 1000;
const int MAXK = 16;
const int MAXQ = 200010;
int n, a[MAXN], b[MAXN], c[MAXN];
struct BinaryIndexedTree {
 public:
  BinaryIndexedTree(int n) {
    N = n;
    t.resize(N + 1);
    for (int i = (0); i <= (N); i++) t[i] = 0;
  }
  void update(int u, int val) {
    while (u <= N) {
      t[u] += val;
      u = u + (u & (-u));
    }
  }
  ll get(int u) {
    ll res = 0;
    while (u) {
      res += t[u];
      u = u - (u & (-u));
    }
    return res;
  }

 private:
  vector<ll> t;
  int N;
};
bool check() {
  for (int i = (1); i <= (n); i++) c[i] = 0;
  for (int i = (1); i <= (n); i++) {
    if (c[a[i]] == 0)
      c[a[i]] = 1;
    else
      return 1;
  }
  BinaryIndexedTree bit(n);
  ll sum = 0;
  for (int i = (n); i >= (1); i--) {
    sum += bit.get(a[i]);
    bit.update(a[i], 1);
  }
  return sum % 2 == 0;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(nullptr);
  int te;
  cin >> te;
  while (te--) {
    cin >> n;
    for (int i = (1); i <= (n); i++) cin >> a[i];
    if (check())
      cout << "YES"
           << "\n";
    else
      cout << "NO\n";
  }
  return 0;
}

```