#include <bits/stdc++.h>
using namespace std;
using INT = int;
template <class T>
using refT = reference_wrapper<T>;
template <class T>
using crefT = reference_wrapper<const T>;
auto &_ = std::ignore;
using ll = long long;
template <class T>
using vec = vector<T>;
template <bool B, class T = void>
using enableif_t = typename enable_if<B, T>::type;
template <class U>
struct canOut {
  template <class T>
  constexpr static auto is(int i) -> decltype((cout << *(T *)(0)), true) {
    return true;
  }
  template <class T>
  constexpr static bool is(...) {
    return false;
  }
  static const bool value = is<U>(1);
};
template <class U>
struct canFor {
  template <class T>
  constexpr static auto is(int i) -> decltype(begin(*(T *)(0)), true) {
    return true;
  }
  template <class T>
  constexpr static bool is(...) {
    return false;
  }
  static const bool value = is<U>(1);
};
constexpr struct {
  template <class T>
  constexpr operator T() const {
    return numeric_limits<T>::max();
  }
} INF;
constexpr struct {
  template <class T>
  constexpr operator T() const {
    return numeric_limits<T>::min();
  }
} MINF;
template <size_t i, class T>
auto operator>>(istream &is, T &r)
    -> decltype(enableif_t<i == tuple_size<T>::value>(1), is) {
  return is;
}
template <size_t i = 0, class T>
auto operator>>(istream &is, T &r)
    -> decltype(enableif_t<i != tuple_size<T>::value>(1), is) {
  is >> get<i>(r);
  return operator>><i + 1>(is, r);
}
template <class T>
auto __format(ostream &os, const char *c, const T &cv)
    -> decltype(enableif_t<canOut<T>::value>(1), c + 1) {
  os << cv;
  while (*c != '}') c++;
  return c + 1;
}
template <size_t i, class T>
auto __format(ostream &os, const char *c, const T &cv)
    -> decltype(enableif_t<!canFor<T>::value>(1),
                enableif_t<i == tuple_size<T>::value>(1), c + 1) {
  return c;
}
template <size_t i = 0, class T>
auto __format(ostream &os, const char *c, const T &cv)
    -> decltype(enableif_t<!canFor<T>::value>(1),
                enableif_t<i != tuple_size<T>::value>(1), c + 1) {
  while (*c != '{') os << *c++;
  c = __format(os, c, get<i>(cv));
  return __format<i + 1>(os, c, cv);
}
template <class T>
auto __format(ostream &os, const char *c, const T &cv)
    -> decltype(enableif_t<!canOut<T>::value>(1),
                enableif_t<canFor<T>::value>(1), c + 1) {
  const char *ct = c + 1;
  if (cv.size() == 0) {
    while (*ct != '}') ct++;
    ct++;
    while (*ct != '}') ct++;
  } else {
    for (auto &i : cv) {
      const char *cc = c + 1;
      while (*cc != '{') os << *cc++;
      cc = __format(os, cc, i);
      while (*cc != '}') os << *cc++;
      ct = cc;
    }
  }
  return ct + 1;
}
void _format(ostream &os, const char *c) {
  while (*c != '{' && *c != '\0') os << *c++;
}
template <class T, class... Args>
void _format(ostream &os, const char *c, const T &a, Args &&...rest) {
  while (*c != '{' && *c != '\0') os << *c++;
  if (*c == '{') c = __format(os, c, a);
  _format(os, c, forward<Args>(rest)...);
}
template <class... Args>
string format(const char *c, Args &&...rest) {
  ostringstream os;
  _format(os, c, forward<Args>(rest)...);
  return os.str();
}
template <class... Args>
ostream &print(const char *c, Args &&...rest) {
  return _format(cout, c, forward<Args>(rest)...), cout;
}
template <class T, class... Args>
struct Rtar {
  T &a;
  tuple<Args...> n;
  Rtar(T &a, tuple<Args...> n) : a(a), n(n) {}
};
template <class T, class... Args>
Rtar<T, Args &...> rtar(T &a, Args &...rest) {
  return Rtar<T, Args &...>(a, tie(rest...));
}
template <size_t i, class U, class... Args, class T = tuple<Args &...>>
auto operator>>(istream &is, Rtar<U, Args &...> r)
    -> decltype(enableif_t<i == tuple_size<T>::value>(1), is) {
  return is >> r.a;
}
template <size_t i = 0, class U, class... Args, class T = tuple<Args &...>>
auto operator>>(istream &is, Rtar<U, Args &...> r)
    -> decltype(enableif_t<i != tuple_size<T>::value>(1), is) {
  r.a = typename decay<U>::type(get<i>(r.n));
  for (auto &w : r.a)
    operator>><i + 1>(is, Rtar<decltype(w), Args &...>(w, r.n));
  return is;
}
template <class T1, class T2>
bool cmin(T1 &a, const T2 b) {
  return a > b ? a = b, 1 : 0;
}
template <class T1, class T2>
bool cmax(T1 &a, const T2 b) {
  return a < b ? a = b, 1 : 0;
}
template <class T1, class T2, class... T3>
bool cmin(T1 &a, const T2 b, const T3... rest) {
  return cmin(a, b) | cmin(a, rest...);
}
template <class T1, class T2, class... T3>
bool cmax(T1 &a, const T2 b, const T3... rest) {
  return cmax(a, b) | cmax(a, rest...);
}
bool MULTIDATA = true;
struct solution {
  int n;
  vector<int> v;
  void scan() { cin >> n >> rtar(v, n); }
  void solve() {
    int a1 = n / 2, a0 = n - a1;
    array<int, 2> c = {};
    for (auto i : v) c[i % 2]++;
    ll minn = INF;
    if (c[0] == a0) {
      ll c = 0;
      bool f = 0;
      array<deque<int>, 2> p, q;
      for (int i = 0; i < n; i++) q[v[i] % 2].push_back(i);
      for (int i = 0; i < n; i++, f = !f) {
        c += abs(i - q[f].front());
        q[f].pop_front();
      }
      cmin(minn, c);
    }
    if (c[1] == a0) {
      ll c = 0;
      bool f = 1;
      array<deque<int>, 2> p, q;
      for (int i = 0; i < n; i++) q[v[i] % 2].push_back(i);
      for (int i = 0; i < n; i++, f = !f) {
        c += abs(i - q[f].front());
        q[f].pop_front();
      }
      cmin(minn, c);
    }
    if (minn == (ll)INF)
      cout << -1 << endl;
    else
      cout << minn / 2 << endl;
  }
};
INT main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int T = 1;
  if (MULTIDATA) cin >> (T);
  while (T--) {
    auto a = unique_ptr<solution>(new solution());
    a->scan();
    a->solve();
    if (!cin.good()) break;
  }
  return 0;
}

### Prompt

Your challenge is to write a CPP solution to the following problem:

<image>

William has an array of n integers a_1, a_2, ..., a_n. In one move he can swap two neighboring items. Two items a_i and a_j are considered neighboring if the condition |i - j| = 1 is satisfied.

William wants you to calculate the minimal number of swaps he would need to perform to make it so that the array does not contain two neighboring items with the same parity.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^4). Description of the test cases follows.

The first line of each test case contains an integer n (1 ≤ n ≤ 10^5) which is the total number of items in William's array.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) which are William's array.

It is guaranteed that the sum of n over all test cases does not exceed 10^5.

Output

For each test case output the minimal number of operations needed or -1 if it is impossible to get the array to a state when no neighboring numbers have the same parity.

Example

Input


5
3
6 6 1
1
9
6
1 1 1 2 2 2
2
8 6
6
6 2 3 4 5 1


Output


1
0
3
-1
2

Note

In the first test case the following sequence of operations would satisfy the requirements: 

  1. swap(2, 3). Array after performing the operation: [6, 1, 6] 



In the second test case the array initially does not contain two neighboring items of the same parity.

In the third test case the following sequence of operations would satisfy the requirements: 

  1. swap(3, 4). Array after performing the operation: [1, 1, 2, 1, 2, 2] 
  2. swap(2, 3). Array after performing the operation: [1, 2, 1, 1, 2, 2] 
  3. swap(4, 5). Array after performing the operation: [1, 2, 1, 2, 1, 2] 



In the fourth test case it is impossible to satisfy the requirements.

In the fifth test case the following sequence of operations would satisfy the requirements: 

  1. swap(2, 3). Array after performing the operation: [6, 3, 2, 4, 5, 1] 
  2. swap(4, 5). Array after performing the operation: [6, 3, 2, 5, 4, 1] 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using INT = int;
template <class T>
using refT = reference_wrapper<T>;
template <class T>
using crefT = reference_wrapper<const T>;
auto &_ = std::ignore;
using ll = long long;
template <class T>
using vec = vector<T>;
template <bool B, class T = void>
using enableif_t = typename enable_if<B, T>::type;
template <class U>
struct canOut {
  template <class T>
  constexpr static auto is(int i) -> decltype((cout << *(T *)(0)), true) {
    return true;
  }
  template <class T>
  constexpr static bool is(...) {
    return false;
  }
  static const bool value = is<U>(1);
};
template <class U>
struct canFor {
  template <class T>
  constexpr static auto is(int i) -> decltype(begin(*(T *)(0)), true) {
    return true;
  }
  template <class T>
  constexpr static bool is(...) {
    return false;
  }
  static const bool value = is<U>(1);
};
constexpr struct {
  template <class T>
  constexpr operator T() const {
    return numeric_limits<T>::max();
  }
} INF;
constexpr struct {
  template <class T>
  constexpr operator T() const {
    return numeric_limits<T>::min();
  }
} MINF;
template <size_t i, class T>
auto operator>>(istream &is, T &r)
    -> decltype(enableif_t<i == tuple_size<T>::value>(1), is) {
  return is;
}
template <size_t i = 0, class T>
auto operator>>(istream &is, T &r)
    -> decltype(enableif_t<i != tuple_size<T>::value>(1), is) {
  is >> get<i>(r);
  return operator>><i + 1>(is, r);
}
template <class T>
auto __format(ostream &os, const char *c, const T &cv)
    -> decltype(enableif_t<canOut<T>::value>(1), c + 1) {
  os << cv;
  while (*c != '}') c++;
  return c + 1;
}
template <size_t i, class T>
auto __format(ostream &os, const char *c, const T &cv)
    -> decltype(enableif_t<!canFor<T>::value>(1),
                enableif_t<i == tuple_size<T>::value>(1), c + 1) {
  return c;
}
template <size_t i = 0, class T>
auto __format(ostream &os, const char *c, const T &cv)
    -> decltype(enableif_t<!canFor<T>::value>(1),
                enableif_t<i != tuple_size<T>::value>(1), c + 1) {
  while (*c != '{') os << *c++;
  c = __format(os, c, get<i>(cv));
  return __format<i + 1>(os, c, cv);
}
template <class T>
auto __format(ostream &os, const char *c, const T &cv)
    -> decltype(enableif_t<!canOut<T>::value>(1),
                enableif_t<canFor<T>::value>(1), c + 1) {
  const char *ct = c + 1;
  if (cv.size() == 0) {
    while (*ct != '}') ct++;
    ct++;
    while (*ct != '}') ct++;
  } else {
    for (auto &i : cv) {
      const char *cc = c + 1;
      while (*cc != '{') os << *cc++;
      cc = __format(os, cc, i);
      while (*cc != '}') os << *cc++;
      ct = cc;
    }
  }
  return ct + 1;
}
void _format(ostream &os, const char *c) {
  while (*c != '{' && *c != '\0') os << *c++;
}
template <class T, class... Args>
void _format(ostream &os, const char *c, const T &a, Args &&...rest) {
  while (*c != '{' && *c != '\0') os << *c++;
  if (*c == '{') c = __format(os, c, a);
  _format(os, c, forward<Args>(rest)...);
}
template <class... Args>
string format(const char *c, Args &&...rest) {
  ostringstream os;
  _format(os, c, forward<Args>(rest)...);
  return os.str();
}
template <class... Args>
ostream &print(const char *c, Args &&...rest) {
  return _format(cout, c, forward<Args>(rest)...), cout;
}
template <class T, class... Args>
struct Rtar {
  T &a;
  tuple<Args...> n;
  Rtar(T &a, tuple<Args...> n) : a(a), n(n) {}
};
template <class T, class... Args>
Rtar<T, Args &...> rtar(T &a, Args &...rest) {
  return Rtar<T, Args &...>(a, tie(rest...));
}
template <size_t i, class U, class... Args, class T = tuple<Args &...>>
auto operator>>(istream &is, Rtar<U, Args &...> r)
    -> decltype(enableif_t<i == tuple_size<T>::value>(1), is) {
  return is >> r.a;
}
template <size_t i = 0, class U, class... Args, class T = tuple<Args &...>>
auto operator>>(istream &is, Rtar<U, Args &...> r)
    -> decltype(enableif_t<i != tuple_size<T>::value>(1), is) {
  r.a = typename decay<U>::type(get<i>(r.n));
  for (auto &w : r.a)
    operator>><i + 1>(is, Rtar<decltype(w), Args &...>(w, r.n));
  return is;
}
template <class T1, class T2>
bool cmin(T1 &a, const T2 b) {
  return a > b ? a = b, 1 : 0;
}
template <class T1, class T2>
bool cmax(T1 &a, const T2 b) {
  return a < b ? a = b, 1 : 0;
}
template <class T1, class T2, class... T3>
bool cmin(T1 &a, const T2 b, const T3... rest) {
  return cmin(a, b) | cmin(a, rest...);
}
template <class T1, class T2, class... T3>
bool cmax(T1 &a, const T2 b, const T3... rest) {
  return cmax(a, b) | cmax(a, rest...);
}
bool MULTIDATA = true;
struct solution {
  int n;
  vector<int> v;
  void scan() { cin >> n >> rtar(v, n); }
  void solve() {
    int a1 = n / 2, a0 = n - a1;
    array<int, 2> c = {};
    for (auto i : v) c[i % 2]++;
    ll minn = INF;
    if (c[0] == a0) {
      ll c = 0;
      bool f = 0;
      array<deque<int>, 2> p, q;
      for (int i = 0; i < n; i++) q[v[i] % 2].push_back(i);
      for (int i = 0; i < n; i++, f = !f) {
        c += abs(i - q[f].front());
        q[f].pop_front();
      }
      cmin(minn, c);
    }
    if (c[1] == a0) {
      ll c = 0;
      bool f = 1;
      array<deque<int>, 2> p, q;
      for (int i = 0; i < n; i++) q[v[i] % 2].push_back(i);
      for (int i = 0; i < n; i++, f = !f) {
        c += abs(i - q[f].front());
        q[f].pop_front();
      }
      cmin(minn, c);
    }
    if (minn == (ll)INF)
      cout << -1 << endl;
    else
      cout << minn / 2 << endl;
  }
};
INT main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  int T = 1;
  if (MULTIDATA) cin >> (T);
  while (T--) {
    auto a = unique_ptr<solution>(new solution());
    a->scan();
    a->solve();
    if (!cin.good()) break;
  }
  return 0;
}

```