#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pi = pair<int, int>;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using vb = vector<bool>;
using i64 = int64_t;
template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& pr) {
  os << pr.first << " " << pr.second;
  return os;
}
template <class T1>
ostream& operator<<(ostream& os, const vector<T1>& v) {
  for (auto it = v.begin(); it != v.end(); it++) os << (*it) << " ";
  return os;
}
template <class T1>
ostream& operator<<(ostream& os, const set<T1>& s) {
  for (auto it = s.begin(); it != s.end(); it++) os << (*it) << " ";
  return os;
}
template <class T1>
ostream& operator<<(ostream& os, const vector<vector<T1>>& v) {
  for (vector<T1> u : v) {
    for (T1 i : u) cout << i << " ";
    cout << endl;
  }
  return os;
}
template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
  is >> p.first >> p.second;
  return is;
}
template <class T1>
istream& operator>>(istream& is, vector<T1>& v) {
  for (auto& x : v) is >> x;
  return is;
}
istream& operator>>(istream& is, string& s) {
  getline(is, s);
  return is;
}
void __print(int x) { cerr << x; }
template <class T>
using max_heap = priority_queue<T>;
template <class T>
using min_heap = priority_queue<T, vector<T>, greater<T>>;
template <class T>
class SSTree {
 public:
  size_t size;
  T dflt;
  vector<T> t, lz;
  T (*cmb)(T, T);
  SSTree(size_t n, T d, T (*cmb)(T, T)) : size(n), dflt(d), cmb(cmb) {
    t.assign(2 * n, d);
    lz.assign(2 * n, d);
  }
  void build(vector<T> v) {
    int i;
    for (i = 0; i < size; i++) t[size + i] = v[i];
    for (i = size - 1; i > 0; i--) t[i] = cmb(t[i << 1], t[i << 1 | 1]);
  }
  T rangeQuery(int l, int r) {
    T ret = 0;
    for (l += size, r += size; l <= r; l >>= 1, r >>= 1) {
      if (l & 1) ret = cmb(ret, t[l++]);
      if (!(r & 1)) ret = cmb(ret, t[r--]);
    }
    return ret;
  }
  T pointQuery(int q) {
    q += size;
    T ret = 0;
    while (q) {
      ret = cmb(ret, t[q]);
      q >>= 1;
    }
    return ret;
  }
  void rangeUpdate(int l, int r, T v) {
    for (l += size, r += size; l <= r; l >>= 1, r >>= 1) {
      if (l & 1) {
        t[l] = cmb(t[l], v);
        l++;
      }
      if (!(r & 1)) {
        t[r] = cmb(t[r], v);
        r--;
      }
    }
  }
  void pointUpdate(int i, int v) {
    i += size;
    t[i] = v;
    while (i) {
      i >>= 1;
      t[i] = cmb(t[i << 1], t[i << 1 | 1]);
    }
  }
};
unsigned int nextPowerOf2(unsigned int n) {
  n--;
  n |= n >> 1;
  n |= n >> 2;
  n |= n >> 4;
  n |= n >> 8;
  n |= n >> 16;
  n++;
  return n;
}
void solve() {
  int tc;
  cin >> tc;
  while (tc--) {
    int n;
    cin >> n;
    vector<int> a(n);
    cin >> a;
    int nodd = 0, neven = 0;
    set<int> oddpos, evepos, s1, s2;
    for (int i = 0; i < n; i++) {
      if (a[i] % 2 == 0) {
        neven++;
        evepos.insert(i);
      } else {
        nodd++;
        oddpos.insert(i);
      }
    }
    s1 = oddpos;
    s2 = evepos;
    if (abs(nodd - neven) > 1)
      cout << -1 << endl;
    else {
      ll bst = 1e14, ans = 0;
      bool ok = true;
      for (int i = 0; i < n; i++) {
        if (i & 1) {
          if (oddpos.find(i) != oddpos.end())
            continue;
          else {
            auto it = oddpos.lower_bound(i);
            if (it == oddpos.end())
              ok = false;
            else {
              ans += ((*it) - i);
              oddpos.erase(it);
              evepos.insert(*it);
            }
          }
        } else {
          auto it = evepos.lower_bound(i);
          if (it == evepos.end())
            ok = false;
          else {
            ans += ((*it) - i);
            evepos.erase(it);
            oddpos.insert(*it);
          }
        }
      }
      if (ok) bst = min(bst, ans);
      ok = true;
      ans = 0;
      oddpos = s1;
      evepos = s2;
      for (int i = 0; i < n; i++) {
        if (i % 2 == 0) {
          if (oddpos.find(i) != oddpos.end())
            continue;
          else {
            auto it = oddpos.lower_bound(i);
            if (it == oddpos.end())
              ok = false;
            else {
              ans += ((*it) - i);
              oddpos.erase(it);
              evepos.insert(*it);
            }
          }
        } else {
          auto it = evepos.lower_bound(i);
          if (it == evepos.end())
            ok = false;
          else {
            ans += ((*it) - i);
            evepos.erase(it);
            oddpos.insert(*it);
          }
        }
      }
      if (ok) bst = min(bst, ans);
      cout << bst << endl;
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  auto clk_strt = chrono::high_resolution_clock::now();
  solve();
  auto clk_end = chrono::high_resolution_clock::now();
  ;
  return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

<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 ll = long long;
using pi = pair<int, int>;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using vb = vector<bool>;
using i64 = int64_t;
template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& pr) {
  os << pr.first << " " << pr.second;
  return os;
}
template <class T1>
ostream& operator<<(ostream& os, const vector<T1>& v) {
  for (auto it = v.begin(); it != v.end(); it++) os << (*it) << " ";
  return os;
}
template <class T1>
ostream& operator<<(ostream& os, const set<T1>& s) {
  for (auto it = s.begin(); it != s.end(); it++) os << (*it) << " ";
  return os;
}
template <class T1>
ostream& operator<<(ostream& os, const vector<vector<T1>>& v) {
  for (vector<T1> u : v) {
    for (T1 i : u) cout << i << " ";
    cout << endl;
  }
  return os;
}
template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
  is >> p.first >> p.second;
  return is;
}
template <class T1>
istream& operator>>(istream& is, vector<T1>& v) {
  for (auto& x : v) is >> x;
  return is;
}
istream& operator>>(istream& is, string& s) {
  getline(is, s);
  return is;
}
void __print(int x) { cerr << x; }
template <class T>
using max_heap = priority_queue<T>;
template <class T>
using min_heap = priority_queue<T, vector<T>, greater<T>>;
template <class T>
class SSTree {
 public:
  size_t size;
  T dflt;
  vector<T> t, lz;
  T (*cmb)(T, T);
  SSTree(size_t n, T d, T (*cmb)(T, T)) : size(n), dflt(d), cmb(cmb) {
    t.assign(2 * n, d);
    lz.assign(2 * n, d);
  }
  void build(vector<T> v) {
    int i;
    for (i = 0; i < size; i++) t[size + i] = v[i];
    for (i = size - 1; i > 0; i--) t[i] = cmb(t[i << 1], t[i << 1 | 1]);
  }
  T rangeQuery(int l, int r) {
    T ret = 0;
    for (l += size, r += size; l <= r; l >>= 1, r >>= 1) {
      if (l & 1) ret = cmb(ret, t[l++]);
      if (!(r & 1)) ret = cmb(ret, t[r--]);
    }
    return ret;
  }
  T pointQuery(int q) {
    q += size;
    T ret = 0;
    while (q) {
      ret = cmb(ret, t[q]);
      q >>= 1;
    }
    return ret;
  }
  void rangeUpdate(int l, int r, T v) {
    for (l += size, r += size; l <= r; l >>= 1, r >>= 1) {
      if (l & 1) {
        t[l] = cmb(t[l], v);
        l++;
      }
      if (!(r & 1)) {
        t[r] = cmb(t[r], v);
        r--;
      }
    }
  }
  void pointUpdate(int i, int v) {
    i += size;
    t[i] = v;
    while (i) {
      i >>= 1;
      t[i] = cmb(t[i << 1], t[i << 1 | 1]);
    }
  }
};
unsigned int nextPowerOf2(unsigned int n) {
  n--;
  n |= n >> 1;
  n |= n >> 2;
  n |= n >> 4;
  n |= n >> 8;
  n |= n >> 16;
  n++;
  return n;
}
void solve() {
  int tc;
  cin >> tc;
  while (tc--) {
    int n;
    cin >> n;
    vector<int> a(n);
    cin >> a;
    int nodd = 0, neven = 0;
    set<int> oddpos, evepos, s1, s2;
    for (int i = 0; i < n; i++) {
      if (a[i] % 2 == 0) {
        neven++;
        evepos.insert(i);
      } else {
        nodd++;
        oddpos.insert(i);
      }
    }
    s1 = oddpos;
    s2 = evepos;
    if (abs(nodd - neven) > 1)
      cout << -1 << endl;
    else {
      ll bst = 1e14, ans = 0;
      bool ok = true;
      for (int i = 0; i < n; i++) {
        if (i & 1) {
          if (oddpos.find(i) != oddpos.end())
            continue;
          else {
            auto it = oddpos.lower_bound(i);
            if (it == oddpos.end())
              ok = false;
            else {
              ans += ((*it) - i);
              oddpos.erase(it);
              evepos.insert(*it);
            }
          }
        } else {
          auto it = evepos.lower_bound(i);
          if (it == evepos.end())
            ok = false;
          else {
            ans += ((*it) - i);
            evepos.erase(it);
            oddpos.insert(*it);
          }
        }
      }
      if (ok) bst = min(bst, ans);
      ok = true;
      ans = 0;
      oddpos = s1;
      evepos = s2;
      for (int i = 0; i < n; i++) {
        if (i % 2 == 0) {
          if (oddpos.find(i) != oddpos.end())
            continue;
          else {
            auto it = oddpos.lower_bound(i);
            if (it == oddpos.end())
              ok = false;
            else {
              ans += ((*it) - i);
              oddpos.erase(it);
              evepos.insert(*it);
            }
          }
        } else {
          auto it = evepos.lower_bound(i);
          if (it == evepos.end())
            ok = false;
          else {
            ans += ((*it) - i);
            evepos.erase(it);
            oddpos.insert(*it);
          }
        }
      }
      if (ok) bst = min(bst, ans);
      cout << bst << endl;
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  auto clk_strt = chrono::high_resolution_clock::now();
  solve();
  auto clk_end = chrono::high_resolution_clock::now();
  ;
  return 0;
}

```