#include <bits/stdc++.h>
using namespace std;
mt19937_64 rang(
    chrono::high_resolution_clock::now().time_since_epoch().count());
int rng(int lim) {
  uniform_int_distribution<int> uid(0, lim - 1);
  return uid(rang);
}
int mod = 1e9 + 7;
bool isprime(long long int n) {
  for (int i = 2; i <= sqrt(n); i++) {
    if (n % i == 0) {
      return false;
    }
  }
  return true;
}
void binarySearch(long long arr[], long long l, long long r, long long x) {
  while (l <= r) {
    long long m = l + (r - l) / 2;
    if (arr[m] == x) {
      arr[m] = -1;
      return;
    }
    if (arr[m] < x)
      l = m + 1;
    else
      r = m - 1;
  }
}
int tree[100001];
void buildTree(int *a, int *tree, int start, int end, int treeNode) {
  if (start == end) {
    tree[treeNode] = a[start];
    return;
  }
  int mid = (start + end) / 2;
  buildTree(a, tree, start, mid, 2 * treeNode);
  buildTree(a, tree, mid + 1, end, 2 * treeNode + 1);
  tree[treeNode] = tree[2 * treeNode] + tree[2 * treeNode + 1];
}
void updateTree(int *a, int *tree, int start, int end, int treeNode, int idx,
                int val) {
  if (start == end) {
    tree[treeNode] = val;
    a[start] = val;
    return;
  }
  int mid = (start + end) / 2;
  if (idx > mid) {
    updateTree(a, tree, mid + 1, end, 2 * treeNode + 1, idx, val);
  } else {
    updateTree(a, tree, start, mid, 2 * treeNode, idx, val);
  }
  tree[treeNode] = tree[2 * treeNode] + tree[2 * treeNode + 1];
}
int lcs(string s1, string s2) {
  int m = s1.length(), n = s2.length();
  int dp[m + 1][n + 1];
  for (int i = 0; i <= m; i++) dp[i][0] = 0;
  for (int j = 0; j <= n; j++) dp[0][j] = 0;
  for (int i = 1; i <= m; i++) {
    for (int j = 1; j <= n; j++) {
      if (s1[i - 1] == s2[j - 1])
        dp[i][j] = 1 + dp[i - 1][j - 1];
      else
        dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]);
    }
  }
  return dp[m][n];
}
int leftIndex(int tail[], int l, int r, int x) {
  while (r > l) {
    int m = l + (r - l) / 2;
    if (tail[m] >= x)
      r = m;
    else
      l = m + 1;
  }
  return r;
}
int longestSubsequence(int n, int a[]) {
  int len = 1;
  int tail[n];
  tail[0] = a[0];
  int i;
  for (i = 1; i < n; i++) {
    if (a[i] > tail[len - 1]) {
      tail[len] = a[i];
      len++;
    } else {
      int c = leftIndex(tail, 0, len - 1, a[i]);
      tail[c] = a[i];
    }
  }
  return len;
}
int query(int *a, int *tree, int start, int end, int treeNode, int left,
          int right) {
  if (start > right || end < left) {
    return 0;
  }
  if (start >= left && end <= right) {
    return tree[treeNode];
  }
  int mid = (start + end) / 2;
  int ans1 = query(a, tree, start, mid, 2 * treeNode, left, right);
  int ans2 = query(a, tree, mid + 1, end, 2 * treeNode + 1, left, right);
  return ans1 + ans2;
}
void Dfs(vector<int> adj[], int src, vector<bool> &visited) {
  visited[src] = true;
  cout << src << " ";
  for (auto itr : adj[src]) {
    if (visited[itr] == false) {
      Dfs(adj, itr, visited);
    }
  }
  return;
}
vector<string> generate(long long n) {
  vector<string> v;
  queue<string> q;
  for (long long i = 0; i < 26; i++) {
    char word = i + 'a';
    string worde = "";
    worde += word;
    q.push(worde);
  }
  while (n--) {
    string ahead = q.front();
    v.push_back(ahead);
    q.pop();
    for (long long i = 0; i < 26; i++) {
      char word = i + 'a';
      string s1 = ahead;
      s1 += word;
      q.push(s1);
    }
  }
  return v;
}
long long binpow(long long a, long long b) {
  long long ans = 1;
  a %= mod;
  while (b) {
    if (b & 1) ans = (ans * a);
    b /= 2;
    a = (a * a);
    ans %= mod;
    a %= mod;
  }
  return ans;
}
bool isPerfectSquare(long double x) {
  if (x >= 0) {
    long long sr = sqrt(x);
    return (sr * sr == x);
  }
  return false;
}
vector<long long> read(long long n) {
  vector<long long> v(n);
  for (long long i = 0; i < n; i++) {
    cin >> v[i];
  }
  return v;
}
void write(vector<long long> v, long long n) {
  for (long long i = 0; i < n; i++) cout << v[i] << " ";
  cout << endl;
}
long long sum(long long n) {
  long long sum = 0;
  while (n > 0) {
    long long rem = n % 10;
    sum += rem;
    n = n / 10;
  }
  return sum;
}
long long fu(long long a[], long long x[], long long n) {
  vector<long long> o, z;
  for (long long i = 0; i < n; i++) {
    if (a[i] == 1)
      o.push_back(i);
    else
      z.push_back(i);
  }
  long long i1 = 0, i2 = 0;
  long long c = 0;
  for (long long i = 0; i < n; i++) {
    if (a[i] != x[i]) {
      if (x[i] == 1) {
        c = c + o[i1] - i;
        a[i] = 1;
        a[o[i1]] = 0;
        i1++;
      } else {
        c = c + z[i2] - i;
        a[i] = 0;
        a[z[i2]] = 1;
        i2++;
      }
    } else {
      if (a[i] == 1) {
        i1++;
      } else
        i2++;
    }
  }
  return c;
}
void solve() {
  long long n;
  cin >> n;
  long long a[n];
  long long o = 0, e = 0;
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
    if (a[i] % 2 == 0) {
      e++;
    } else {
      o++;
    }
    long long p = a[i] % 2;
    a[i] = p;
  }
  if (n == 1) {
    cout << 0 << endl;
    return;
  }
  if (abs(o - e) > 1) {
    cout << -1 << endl;
  } else {
    if (n % 2 == 0) {
      long long x[n];
      long long y[n];
      for (long long i = 0; i < n; i++) {
        if (i % 2 == 0) {
          x[i] = 1;
          y[i] = 0;
        } else {
          x[i] = 0;
          y[i] = 1;
        }
      }
      long long b[n];
      for (long long i = 0; i < n; i++) {
        b[i] = a[i];
      }
      cout << min(fu(a, x, n), fu(b, y, n)) << endl;
    } else {
      long long x[n];
      if (o > e) {
        for (long long i = 0; i < n; i++) {
          if (i % 2 == 0)
            x[i] = 1;
          else
            x[i] = 0;
        }
      } else {
        for (long long i = 0; i < n; i++) {
          if (i % 2 == 0)
            x[i] = 0;
          else
            x[i] = 1;
        }
      }
      cout << fu(a, x, n) << endl;
    }
  }
}
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  srand(chrono::high_resolution_clock::now().time_since_epoch().count());
  long long t;
  cin >> t;
  while (t--) {
    solve();
  }
  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;
mt19937_64 rang(
    chrono::high_resolution_clock::now().time_since_epoch().count());
int rng(int lim) {
  uniform_int_distribution<int> uid(0, lim - 1);
  return uid(rang);
}
int mod = 1e9 + 7;
bool isprime(long long int n) {
  for (int i = 2; i <= sqrt(n); i++) {
    if (n % i == 0) {
      return false;
    }
  }
  return true;
}
void binarySearch(long long arr[], long long l, long long r, long long x) {
  while (l <= r) {
    long long m = l + (r - l) / 2;
    if (arr[m] == x) {
      arr[m] = -1;
      return;
    }
    if (arr[m] < x)
      l = m + 1;
    else
      r = m - 1;
  }
}
int tree[100001];
void buildTree(int *a, int *tree, int start, int end, int treeNode) {
  if (start == end) {
    tree[treeNode] = a[start];
    return;
  }
  int mid = (start + end) / 2;
  buildTree(a, tree, start, mid, 2 * treeNode);
  buildTree(a, tree, mid + 1, end, 2 * treeNode + 1);
  tree[treeNode] = tree[2 * treeNode] + tree[2 * treeNode + 1];
}
void updateTree(int *a, int *tree, int start, int end, int treeNode, int idx,
                int val) {
  if (start == end) {
    tree[treeNode] = val;
    a[start] = val;
    return;
  }
  int mid = (start + end) / 2;
  if (idx > mid) {
    updateTree(a, tree, mid + 1, end, 2 * treeNode + 1, idx, val);
  } else {
    updateTree(a, tree, start, mid, 2 * treeNode, idx, val);
  }
  tree[treeNode] = tree[2 * treeNode] + tree[2 * treeNode + 1];
}
int lcs(string s1, string s2) {
  int m = s1.length(), n = s2.length();
  int dp[m + 1][n + 1];
  for (int i = 0; i <= m; i++) dp[i][0] = 0;
  for (int j = 0; j <= n; j++) dp[0][j] = 0;
  for (int i = 1; i <= m; i++) {
    for (int j = 1; j <= n; j++) {
      if (s1[i - 1] == s2[j - 1])
        dp[i][j] = 1 + dp[i - 1][j - 1];
      else
        dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]);
    }
  }
  return dp[m][n];
}
int leftIndex(int tail[], int l, int r, int x) {
  while (r > l) {
    int m = l + (r - l) / 2;
    if (tail[m] >= x)
      r = m;
    else
      l = m + 1;
  }
  return r;
}
int longestSubsequence(int n, int a[]) {
  int len = 1;
  int tail[n];
  tail[0] = a[0];
  int i;
  for (i = 1; i < n; i++) {
    if (a[i] > tail[len - 1]) {
      tail[len] = a[i];
      len++;
    } else {
      int c = leftIndex(tail, 0, len - 1, a[i]);
      tail[c] = a[i];
    }
  }
  return len;
}
int query(int *a, int *tree, int start, int end, int treeNode, int left,
          int right) {
  if (start > right || end < left) {
    return 0;
  }
  if (start >= left && end <= right) {
    return tree[treeNode];
  }
  int mid = (start + end) / 2;
  int ans1 = query(a, tree, start, mid, 2 * treeNode, left, right);
  int ans2 = query(a, tree, mid + 1, end, 2 * treeNode + 1, left, right);
  return ans1 + ans2;
}
void Dfs(vector<int> adj[], int src, vector<bool> &visited) {
  visited[src] = true;
  cout << src << " ";
  for (auto itr : adj[src]) {
    if (visited[itr] == false) {
      Dfs(adj, itr, visited);
    }
  }
  return;
}
vector<string> generate(long long n) {
  vector<string> v;
  queue<string> q;
  for (long long i = 0; i < 26; i++) {
    char word = i + 'a';
    string worde = "";
    worde += word;
    q.push(worde);
  }
  while (n--) {
    string ahead = q.front();
    v.push_back(ahead);
    q.pop();
    for (long long i = 0; i < 26; i++) {
      char word = i + 'a';
      string s1 = ahead;
      s1 += word;
      q.push(s1);
    }
  }
  return v;
}
long long binpow(long long a, long long b) {
  long long ans = 1;
  a %= mod;
  while (b) {
    if (b & 1) ans = (ans * a);
    b /= 2;
    a = (a * a);
    ans %= mod;
    a %= mod;
  }
  return ans;
}
bool isPerfectSquare(long double x) {
  if (x >= 0) {
    long long sr = sqrt(x);
    return (sr * sr == x);
  }
  return false;
}
vector<long long> read(long long n) {
  vector<long long> v(n);
  for (long long i = 0; i < n; i++) {
    cin >> v[i];
  }
  return v;
}
void write(vector<long long> v, long long n) {
  for (long long i = 0; i < n; i++) cout << v[i] << " ";
  cout << endl;
}
long long sum(long long n) {
  long long sum = 0;
  while (n > 0) {
    long long rem = n % 10;
    sum += rem;
    n = n / 10;
  }
  return sum;
}
long long fu(long long a[], long long x[], long long n) {
  vector<long long> o, z;
  for (long long i = 0; i < n; i++) {
    if (a[i] == 1)
      o.push_back(i);
    else
      z.push_back(i);
  }
  long long i1 = 0, i2 = 0;
  long long c = 0;
  for (long long i = 0; i < n; i++) {
    if (a[i] != x[i]) {
      if (x[i] == 1) {
        c = c + o[i1] - i;
        a[i] = 1;
        a[o[i1]] = 0;
        i1++;
      } else {
        c = c + z[i2] - i;
        a[i] = 0;
        a[z[i2]] = 1;
        i2++;
      }
    } else {
      if (a[i] == 1) {
        i1++;
      } else
        i2++;
    }
  }
  return c;
}
void solve() {
  long long n;
  cin >> n;
  long long a[n];
  long long o = 0, e = 0;
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
    if (a[i] % 2 == 0) {
      e++;
    } else {
      o++;
    }
    long long p = a[i] % 2;
    a[i] = p;
  }
  if (n == 1) {
    cout << 0 << endl;
    return;
  }
  if (abs(o - e) > 1) {
    cout << -1 << endl;
  } else {
    if (n % 2 == 0) {
      long long x[n];
      long long y[n];
      for (long long i = 0; i < n; i++) {
        if (i % 2 == 0) {
          x[i] = 1;
          y[i] = 0;
        } else {
          x[i] = 0;
          y[i] = 1;
        }
      }
      long long b[n];
      for (long long i = 0; i < n; i++) {
        b[i] = a[i];
      }
      cout << min(fu(a, x, n), fu(b, y, n)) << endl;
    } else {
      long long x[n];
      if (o > e) {
        for (long long i = 0; i < n; i++) {
          if (i % 2 == 0)
            x[i] = 1;
          else
            x[i] = 0;
        }
      } else {
        for (long long i = 0; i < n; i++) {
          if (i % 2 == 0)
            x[i] = 0;
          else
            x[i] = 1;
        }
      }
      cout << fu(a, x, n) << endl;
    }
  }
}
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  srand(chrono::high_resolution_clock::now().time_since_epoch().count());
  long long t;
  cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}

```