#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
using namespace std;
using ll = long long;
using VI = vector<ll>;
using VV = vector<VI>;
using VS = vector<string>;
using PII = pair<ll, ll>;
template <typename A, typename B>
string to_string(pair<A, B> p);
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
string to_string(const string& s) { return '"' + s + '"'; }
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
string to_string(char c) {
  string s = {c};
  return s;
}
string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}
template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto& x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
void debug_out() { cerr << '\n'; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
template <class T>
bool chmax(T& a, const T& b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmin(T& a, const T& b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
void yes() {
  cout << ("Yes") << '\n';
  exit(0);
}
void no() {
  cout << ("No") << '\n';
  exit(0);
}
void possible() {
  cout << ("Possible") << '\n';
  exit(0);
}
void impossible() {
  cout << ("Impossible") << '\n';
  exit(0);
}
ll SUM(VI& V) { return accumulate((V).begin(), (V).end(), 0LL); }
ll MIN(VI& V) { return *min_element((V).begin(), (V).end()); }
ll MAX(VI& V) { return *max_element((V).begin(), (V).end()); }
void print_vector(VI& V, ll offset = 0) {
  ll n = V.size();
  for (ll i = (0); i < (n); ++i) {
    if (i) cout << ' ';
    cout << V[i] + offset;
  }
  cout << endl;
}
ll gcd(ll a, ll b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
ll lcm(ll a, ll b) {
  ll g = gcd(a, b);
  return a / g * b;
}
using ld = long double;
using inverse_priority_queue = priority_queue<ll, vector<ll>, greater<ll> >;
int popcount(ll t) { return __builtin_popcountll(t); }
const ll mod = 1e9 + 7;
const ll inf = 1e18;
const double PI = acos(-1);
ll ceil_div(ll a, ll b) { return (a + b - 1) / b; }
ll ll_pow(ll a, ll n) {
  ll ans = 1;
  for (ll i = (0); i < (n); ++i) {
    ans *= a;
  }
  return ans;
}
struct mint {
  ll x;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint& operator+=(const mint a) {
    if ((x += a.x) >= mod) x -= mod;
    return *this;
  }
  mint& operator-=(const mint a) {
    if ((x += mod - a.x) >= mod) x -= mod;
    return *this;
  }
  mint& operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res *= a;
  }
  mint pow(ll t) const {
    if (!t) return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1) a *= *this;
    return a;
  }
  mint inv() const { return pow(mod - 2); }
  mint& operator/=(const mint a) { return (*this) *= a.inv(); }
  mint operator/(const mint a) const {
    mint res(*this);
    return res /= a;
  }
};
void solve() {
  ll N;
  cin >> N;
  VI A(N);
  for (ll i = (0); i < (N); ++i) {
    cin >> A[i];
    A[i]--;
  }
  auto key = [&](ll i, ll j) { return N * A[i] + A[j]; };
  VI C(N * N);
  for (ll i = (1); i < (N); ++i) {
    for (ll j = (i + 1); j < (N); ++j) {
      C[key(i, j)]++;
    }
  }
  ll sum = 0;
  for (ll j = (1); j < (N - 2); ++j) {
    for (ll k = (j + 1); k < (N); ++k) {
      C[key(j, k)]--;
    }
    for (ll i = (0); i < (j); ++i) {
      sum += C[key(i, j)];
    }
  }
  cout << (sum) << '\n';
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  ll N;
  cin >> N;
  while (N--) solve();
  return 0;
}

### Prompt

Generate a Cpp solution to the following problem:

You are given an array a_1, a_2 ... a_n. Calculate the number of tuples (i, j, k, l) such that: 

  * 1 ≤ i < j < k < l ≤ n; 
  * a_i = a_k and a_j = a_l; 

Input

The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases.

The first line of each test case contains a single integer n (4 ≤ n ≤ 3000) — the size of the array a.

The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ n) — the array a.

It's guaranteed that the sum of n in one test doesn't exceed 3000.

Output

For each test case, print the number of described tuples.

Example

Input


2
5
2 2 2 2 2
6
1 3 3 1 2 3


Output


5
2

Note

In the first test case, for any four indices i < j < k < l are valid, so the answer is the number of tuples.

In the second test case, there are 2 valid tuples: 

  * (1, 2, 4, 6): a_1 = a_4 and a_2 = a_6; 
  * (1, 3, 4, 6): a_1 = a_4 and a_3 = a_6. 

### Response

```cpp
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
using namespace std;
using ll = long long;
using VI = vector<ll>;
using VV = vector<VI>;
using VS = vector<string>;
using PII = pair<ll, ll>;
template <typename A, typename B>
string to_string(pair<A, B> p);
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
string to_string(const string& s) { return '"' + s + '"'; }
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
string to_string(char c) {
  string s = {c};
  return s;
}
string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}
template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto& x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
void debug_out() { cerr << '\n'; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
template <class T>
bool chmax(T& a, const T& b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmin(T& a, const T& b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}
void yes() {
  cout << ("Yes") << '\n';
  exit(0);
}
void no() {
  cout << ("No") << '\n';
  exit(0);
}
void possible() {
  cout << ("Possible") << '\n';
  exit(0);
}
void impossible() {
  cout << ("Impossible") << '\n';
  exit(0);
}
ll SUM(VI& V) { return accumulate((V).begin(), (V).end(), 0LL); }
ll MIN(VI& V) { return *min_element((V).begin(), (V).end()); }
ll MAX(VI& V) { return *max_element((V).begin(), (V).end()); }
void print_vector(VI& V, ll offset = 0) {
  ll n = V.size();
  for (ll i = (0); i < (n); ++i) {
    if (i) cout << ' ';
    cout << V[i] + offset;
  }
  cout << endl;
}
ll gcd(ll a, ll b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
ll lcm(ll a, ll b) {
  ll g = gcd(a, b);
  return a / g * b;
}
using ld = long double;
using inverse_priority_queue = priority_queue<ll, vector<ll>, greater<ll> >;
int popcount(ll t) { return __builtin_popcountll(t); }
const ll mod = 1e9 + 7;
const ll inf = 1e18;
const double PI = acos(-1);
ll ceil_div(ll a, ll b) { return (a + b - 1) / b; }
ll ll_pow(ll a, ll n) {
  ll ans = 1;
  for (ll i = (0); i < (n); ++i) {
    ans *= a;
  }
  return ans;
}
struct mint {
  ll x;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint& operator+=(const mint a) {
    if ((x += a.x) >= mod) x -= mod;
    return *this;
  }
  mint& operator-=(const mint a) {
    if ((x += mod - a.x) >= mod) x -= mod;
    return *this;
  }
  mint& operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res *= a;
  }
  mint pow(ll t) const {
    if (!t) return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1) a *= *this;
    return a;
  }
  mint inv() const { return pow(mod - 2); }
  mint& operator/=(const mint a) { return (*this) *= a.inv(); }
  mint operator/(const mint a) const {
    mint res(*this);
    return res /= a;
  }
};
void solve() {
  ll N;
  cin >> N;
  VI A(N);
  for (ll i = (0); i < (N); ++i) {
    cin >> A[i];
    A[i]--;
  }
  auto key = [&](ll i, ll j) { return N * A[i] + A[j]; };
  VI C(N * N);
  for (ll i = (1); i < (N); ++i) {
    for (ll j = (i + 1); j < (N); ++j) {
      C[key(i, j)]++;
    }
  }
  ll sum = 0;
  for (ll j = (1); j < (N - 2); ++j) {
    for (ll k = (j + 1); k < (N); ++k) {
      C[key(j, k)]--;
    }
    for (ll i = (0); i < (j); ++i) {
      sum += C[key(i, j)];
    }
  }
  cout << (sum) << '\n';
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  ll N;
  cin >> N;
  while (N--) solve();
  return 0;
}

```