Captain Marmot wants to prepare a huge and important battle against his enemy, Captain Snake. For this battle he has n regiments, each consisting of 4 moles.

Initially, each mole i (1 ≤ i ≤ 4n) is placed at some position (xi, yi) in the Cartesian plane. Captain Marmot wants to move some moles to make the regiments compact, if it's possible.

Each mole i has a home placed at the position (ai, bi). Moving this mole one time means rotating his position point (xi, yi) 90 degrees counter-clockwise around it's home point (ai, bi).

A regiment is compact only if the position points of the 4 moles form a square with non-zero area.

Help Captain Marmot to find out for each regiment the minimal number of moves required to make that regiment compact, if it's possible.

Input

The first line contains one integer n (1 ≤ n ≤ 100), the number of regiments.

The next 4n lines contain 4 integers xi, yi, ai, bi ( - 104 ≤ xi, yi, ai, bi ≤ 104).

Output

Print n lines to the standard output. If the regiment i can be made compact, the i-th line should contain one integer, the minimal number of required moves. Otherwise, on the i-th line print "-1" (without quotes).

Examples

Input

4
1 1 0 0
-1 1 0 0
-1 1 0 0
1 -1 0 0
1 1 0 0
-2 1 0 0
-1 1 0 0
1 -1 0 0
1 1 0 0
-1 1 0 0
-1 1 0 0
-1 1 0 0
2 2 0 1
-1 0 0 -2
3 0 0 -2
-1 1 -2 0


Output

1
-1
3
3

Note

In the first regiment we can move once the second or the third mole.

We can't make the second regiment compact.

In the third regiment, from the last 3 moles we can move once one and twice another one.

In the fourth regiment, we can move twice the first mole and once the third mole.
import java.io.*;
import java.util.*;
import java.util.zip.ZipEntry;
import java.math.*;

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Input in = new Input(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(1, in, out);
        out.close();
    }
}

class Task {
    static final long MOD = 1000000007;
    int[] primes;

    public void solve(int testNumber, Input in, PrintWriter out) {
        int n = in.nextInt();
        int[][] m = new int[4][4];
        for (int t = 0; t < n; t++) {
            for (int i = 0; i < 4; i++) {
                for (int j = 0; j < 4; j++) {
                    m[i][j] = in.nextInt();
                }
            }
            int ans = Integer.MAX_VALUE;
            for (int i = 0; i < 4; i++) {
                for (int j = 0; j < 4; j++) {
                    for (int k = 0; k < 4; k++) {
                        for (int l = 0; l < 4; l++) {
                            if (isQuare(m)) {
                                ans = Math.min(ans, i + j + k + l);
                            }
                            rotate(m, 3);
                        }
                        rotate(m, 2);
                    }
                    rotate(m, 1);
                }
                rotate(m, 0);
            }
            out.println(ans == Integer.MAX_VALUE ? -1 : ans);
        }
    }

    private boolean isQuare(int[][] m) {
        long[] dist = new long[6];
        int index = 0;
        for (int i = 0; i < 4; i++) {
            for (int j = i + 1; j < 4; j++) {
                dist[index++] = dist(m[i][0], m[i][1], m[j][0], m[j][1]);
            }
        }
        Arrays.sort(dist);
        if (dist[0] == 0 || dist[5] == 0)
            return false;
        for (int i = 0; i < 2; i++) {
            if (dist[i] != dist[i + 1])
                return false;
        }

        return dist[4] == dist[5];
    }

    private long dist(long x1, long y1, long x2, long y2) {
        return (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);
    }

    static void rotate(int[][] m, int row) {
        int x = m[row][0] - m[row][2];
        int y = m[row][1] - m[row][3];
        m[row][0] = m[row][2] - y;
        m[row][1] = m[row][3] + x;
    }

    // didn't test
    static class BIT {
        int[] MAX;
        int[] MIN;
        int[] SUM;
        int n;

        public BIT(int n) {
            MAX = new int[n + 1];
            MIN = new int[n + 1];
            SUM = new int[n + 1];
            this.n = n;
        }

        public void setSum(int pos, int val) {
            for (int i = pos; i < n; i += (i & -i)) {
                SUM[i] += val;
            }
        }

        public int getSum(int to) {
            int sum = 0;
            for (int i = to; i > 0; i -= (i & -i)) {
                sum += SUM[i];
            }
            return sum;
        }

        public int getSum(int from, int to) {
            return getSum(to) - getSum(from);
        }

        public void setMax(int pos, int val) {
            for (int i = pos; i < n; i += (i & -i)) {
                MAX[i] = Math.max(val, MAX[i]);
            }
        }

        public int getMax(int to) {
            int max = 0;
            for (int i = to; i > 0; i -= (i & -i)) {
                max = Math.max(max, MAX[i]);
            }
            return max;
        }

        public void setMin(int pos, int val) {
            for (int i = pos; i < n; i += (i & -i)) {
                MIN[i] = Math.min(val, MIN[i]);
            }
        }

        public int getMin(int to) {
            int min = 0;
            for (int i = to; i > 0; i -= (i & -i)) {
                min = Math.min(min, MIN[i]);
            }
            return min;
        }

    }

    // didn't test
    static class DisjointSet {
        int[] set;

        public DisjointSet(int n) {
            set = new int[n];
            for (int i = 0; i < n; i++) {
                set[i] = i;
            }
        }

        public int findSet(int a) {
            if (set[a] == a)
                return a;
            return findSet(set[a]);
        }

        public void unionSet(int a, int b) {
            set[findSet(a)] = findSet(b);
        }

        public boolean isSameSet(int a, int b) {
            return findSet(a) == findSet(b);
        }
    }

    static class SegmentTree {
        int[] MAX;
        int[] MIN;
        int[] SUM;
        int[] data;
        int n;

        public SegmentTree(int[] data) {
            this.n = data.length;
            this.data = data;
            MAX = new int[4 * n + 10];
            MIN = new int[4 * n + 10];
            SUM = new int[4 * n + 10];
            buildTree(1, 0, n - 1);
        }

        public int left(int root) {
            return root << 1;
        }

        public int right(int root) {
            return (root << 1) + 1;
        }

        private void buildTree(int root, int rl, int rr) {
            if (rr == rl) {
                MAX[root] = MIN[root] = SUM[root] = data[rr];
            } else {
                int rm = (rl + rr) >> 1;
                buildTree(left(root), rl, rm);
                buildTree(right(root), rm + 1, rr);
                MAX[root] = Math.max(MAX[left(root)], MAX[right(root)]);
                MIN[root] = Math.min(MIN[left(root)], MIN[right(root)]);
                SUM[root] = SUM[left(root)] + SUM[right(root)];
            }
        }

        public int getMax(int from, int to) {
            return getMax(1, 0, n - 1, from, to);
        }

        private int getMax(int root, int rl, int rr, int from, int to) {
            if (from > rr || to < rl || rl > rr) {
                return -1;
            }
            if (from == rl && to == rr) {
                return MAX[root];
            }
            int rm = (rr + rl) >> 1;
            int m1 = getMax(left(root), rl, rm, from, Math.min(to, rm));
            int m2 = getMax(right(root), rm + 1, rr, Math.max(from, rm + 1), to);
            return Math.max(m1, m2);
        }

        public int getMin(int from, int to) {
            return getMin(1, 0, n - 1, from, to);
        }

        private int getMin(int root, int rl, int rr, int from, int to) {
            if (from > rr || to < rl || rl > rr) {
                return Integer.MAX_VALUE;
            }
            if (from == rl && to == rr) {
                return MIN[root];
            }
            int rm = (rr + rl) >> 1;
            int m1 = getMin(left(root), rl, rm, from, Math.min(to, rm));
            int m2 = getMin(right(root), rm + 1, rr, Math.max(from, rm + 1), to);
            return Math.min(m1, m2);
        }

        public int getSum(int from, int to) {
            return getSum(1, 0, n - 1, from, to);
        }

        private int getSum(int root, int rl, int rr, int from, int to) {
            if (from > rr || to < rl || rl > rr) {
                return 0;
            }
            if (from == rl && to == rr) {
                return SUM[root];
            }
            int rm = (rr + rl) >> 1;
            int m1 = getSum(left(root), rl, rm, from, Math.min(to, rm));
            int m2 = getSum(right(root), rm + 1, rr, Math.max(from, rm + 1), to);
            return m1 + m2;
        }
    }

    private String lcs(String s1, String s2) {
        int n = s1.length();
        int m = s2.length();
        int[][] dp = new int[n + 1][m + 1];
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                if (s1.charAt(i - 1) == s2.charAt(j - 1)) {
                    dp[i][j] = dp[i - 1][j - 1] + 1;
                } else {
                    dp[i][j] = Math.max(dp[i - 1][j], dp[i][j - 1]);
                }
            }
        }
        StringBuilder sb = new StringBuilder();
        int i = n;
        int j = m;
        while (i > 0 && j > 0) {
            if (s1.charAt(i - 1) == s2.charAt(j - 1)) {
                sb.append(s1.charAt(i - 1));
                i--;
                j--;
            } else {
                if (dp[i - 1][j] > dp[i][j - 1]) {
                    i--;
                } else {
                    j--;
                }
            }
        }
        return sb.reverse().toString();
    }

    private boolean isPrime(int n) {
        if (n <= 3)
            return n > 1;
        else if (n % 3 == 0 || n % 2 == 0)
            return false;
        for (long i = 5; i * i <= n; i += 6) {
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
        }
        return true;
    }

    private int[] getPrimes(int n) {
        int len = n + 1;
        boolean[] isPrimes = new boolean[len];
        int[] temps = new int[len];
        int index = 0;
        Arrays.fill(isPrimes, true);
        isPrimes[0] = isPrimes[1] = false;
        for (int i = 2; i * i < len; i++) {
            if (isPrimes[i]) {
                for (int j = i * i; j < len; j += i) {
                    isPrimes[j] = false;
                }
            }
        }
        for (int i = 0; i < len; i++) {
            if (isPrimes[i])
                temps[index++] = i;
        }
        int[] primes = Arrays.copyOf(temps, index);
        return primes;
    }

    static void swap(char[] arrays, int pos1, int pos2) {
        char tmp = arrays[pos1];
        arrays[pos1] = arrays[pos2];
        arrays[pos2] = tmp;
    }

    static void swap(int[] arrays, int pos1, int pos2) {
        int tmp = arrays[pos1];
        arrays[pos1] = arrays[pos2];
        arrays[pos2] = tmp;
    }

    static long modPow(long n, long ex) {
        long res = 1;
        while (ex > 0) {
            if ((ex & 1) == 1)
                res = res * n % MOD;
            n = n * n % MOD;
            ex >>= 1;
        }
        return res;
    }

    static long ModInverse(long n) {
        return modPow(n, MOD - 2);
    }

    static long nCr(int n, int r) {
        if (r > n)
            return -1;
        // return (f[n] * ModInverse((f[r] * f[n - r]) % MOD)) % MOD;
        return 0;
    }
}

class Input {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public Input(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }
}
