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.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.*;
import java.util.concurrent.LinkedBlockingDeque;
import java.io.FileWriter;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.LinkedList;


// graph, dfs,bfs, get connected components,iscycle, isbipartite, dfs on trees



public class scratch_25 {
    static class Graph{

        public static class Vertex{
            HashMap<Integer,Integer> nb= new HashMap<>();     // for neighbours of each vertex
        }

        public static HashMap<Integer,Vertex> vt;   // for vertices(all)

        public Graph(){
            vt= new HashMap<>();
        }

        public static int numVer(){
            return vt.size();
        }

        public static boolean contVer(int ver){
            return vt.containsKey(ver);
        }

        public static void addVer(int ver){
            Vertex v= new Vertex();
            vt.put(ver,v);
        }






        public static void addEdge(int ver1, int ver2, int weight){
            if(!vt.containsKey(ver1) || !vt.containsKey(ver2)){
                return;
            }
            Vertex v1= vt.get(ver1);
            Vertex v2= vt.get(ver2);
            v1.nb.put(ver2,weight);                                 // if previously there is an edge, then this replaces that edge
            v2.nb.put(ver1,weight);
        }

        public static void delEdge(int ver1, int ver2){

            if(!vt.containsKey(ver1) || !vt.containsKey(ver2)){
                return;
            }
            vt.get(ver1).nb.remove(ver2);
            vt.get(ver2).nb.remove(ver1);
        }
        public static void delVer(int ver){
            if(!vt.containsKey(ver)){
                return;
            }
            Vertex v1= vt.get(ver);
            ArrayList<Integer> arr= new ArrayList<>(v1.nb.keySet());
            for (int i = 0; i <arr.size() ; i++) {
                int s= arr.get(i);
                vt.get(s).nb.remove(ver);
            }
            vt.remove(ver);
        }
        static boolean done[];
        static int parent[];
        static ArrayList<Integer>vals= new ArrayList<>();


        public static boolean isCycle(int i){
            Stack<Integer>stk= new Stack<>();

            stk.push(i);
            while(!stk.isEmpty()){
                int x= stk.pop();
                vals.add(x);
                //   System.out.print("current="+x+" stackinit="+stk);
                if(!done[x]){
                    done[x]=true;
                }
                else if(done[x] ){
                    return true;
                }

                ArrayList<Integer>ar= new ArrayList<>(vt.get(x).nb.keySet());
                for (int j = 0; j <ar.size() ; j++) {
                    if(parent[x]!=ar.get(j)){
                        parent[ar.get(j)]=x;
                        stk.push(ar.get(j));
                    }
                }
                // System.out.println(" stackfin="+stk);
            }
            return false;
        }
        static int[]level;
        static int[] curr;
        static int[] fin;

        public static void dfs(int src){
            done[src]=true;
            level[src]=0;
            Queue<Integer>q= new LinkedList<>();
            q.add(src);
            while(!q.isEmpty()){
                int x= q.poll();
                ArrayList<Integer>arr= new ArrayList<>(vt.get(x).nb.keySet());
                for (int i = 0; i <arr.size() ; i++) {
                    int v= arr.get(i);
                    if(!done[v]){
                        level[v]=level[x]+1;
                        done[v]=true;
                        q.offer(v);
                    }
                }
            }
        }
        static int oc[];
        static int ec[];


        public static void dfs1(int src){
            Queue<Integer>q= new LinkedList<>();
            q.add(src);
            done[src]= true;
            //    int count=0;
            while(!q.isEmpty()){

                int x= q.poll();
                //   System.out.println("x="+x);
                int even= ec[x];
                int odd= oc[x];
                if(level[x]%2==0){
                    int val= (curr[x]+even)%2;
                    if(val!=fin[x]){
                        //  System.out.println("bc");
                        even++;
                        vals.add(x);
                    }
                }
                else{
                    int val= (curr[x]+odd)%2;
                    if(val!=fin[x]){
                        //   System.out.println("bc");
                        odd++;
                        vals.add(x);
                    }

                }
                ArrayList<Integer>arr= new ArrayList<>(vt.get(x).nb.keySet());
                //   System.out.println(arr);
                for (int i = 0; i <arr.size() ; i++) {
                    int v= arr.get(i);
                    if(!done[v]){
                        done[v]=true;
                        oc[v]=odd;
                        ec[v]=even;
                        q.add(v);
                    }
                }
            }

        }

        static long popu[];
        static long happy[];
        static long count[]; // total people crossing that pos
        static long sum[]; // total sum of happy people including that.


        public static void bfs(int x){
            done[x]=true;
            long total= popu[x];
//            long smile= happy[x];
            ArrayList<Integer>nbrs= new ArrayList<>(vt.get(x).nb.keySet());
            for (int i = 0; i <nbrs.size() ; i++) {
                int r= nbrs.get(i);
                if(!done[r]){
                    bfs(r);
                    total+=count[r];
//                    smile+=sum[r];
                }
            }
            count[x]=total;
//            sum[x]=smile;
        }


        public static void bfs1(int x){
            done[x]=true;
//            long total= popu[x];
            long smile= 0;
            ArrayList<Integer>nbrs= new ArrayList<>(vt.get(x).nb.keySet());
            for (int i = 0; i <nbrs.size() ; i++) {
                int r= nbrs.get(i);
                if(!done[r]){
                    bfs1(r);
//                    total+=count[r];
                    smile+=happy[r];
                }
            }
//            count[x]=total;
            sum[x]=smile;
        }


    }




    static class Reader {
        static BufferedReader reader;
        static StringTokenizer tokenizer;

        /**
         * call this method to initialize reader for InputStream
         */
        static void init(InputStream input) {
            reader = new BufferedReader(
                    new InputStreamReader(input));
            tokenizer = new StringTokenizer("");
        }

        /**
         * get next word
         */
        static String next() throws IOException {
            while (!tokenizer.hasMoreTokens()) {
                //TODO add check for eof if necessary
                tokenizer = new StringTokenizer(
                        reader.readLine());
            }
            return tokenizer.nextToken();
        }

        static int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        static double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        static long nextLong() throws IOException {
            return Long.parseLong(next());
        }
    }


    static class Pair implements Comparable<Pair> {
        long x;
        long y;


        public Pair(long x, long y) {
            this.x = x;
            this.y = y;

        }


        @Override
        public String toString() {
            return x + " " + y;
        }

        @Override
        public int compareTo(Pair o) {
            if(this.x >o.x){
                return 1;
            }
            else if(this.x==o.x){
                return 0;
            }
            else{
                return -1;
            }
        }
    }

    // After writing solution, quick scan for:
    //   array out of bounds
    //   special cases e.g. n=1?
    //
    // Big numbers arithmetic bugs:
    //   int overflow
    //   sorting, or taking max, or negative after MOD


    public static void main(String[] args)  throws IOException {
        Reader.init(System.in);
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
        int t= Reader.nextInt();
        for (int tt = 0; tt <t ; tt++) {
            long arr[][]= new long[4][4];
            for (int i = 0; i <4 ; i++) {
                for (int j = 0; j <4 ; j++) {
                    arr[i][j]= Reader.nextLong();
                }}

//            for (int i = 0; i <4 ; i++) {
//                System.out.println(Arrays.toString(arr[i]));
//            }
//            System.out.println();
            Pair places[][]= new Pair[4][4];
            for (int i = 0; i <4 ; i++) {
                long x= arr[i][0];
                long y= arr[i][1];
                long px= arr[i][2];
                long py= arr[i][3];
                x-=px;
                y-=py;
                long x1=x;
                long y1=y;
                places[i][1]= new Pair(-1*y+px,x+py);
                places[i][0]= new Pair(x+px,y+py);
                places[i][2]= new Pair(-1*x+px,-1*y+py);
                places[i][3]= new Pair(y+px,-1*x+py);
            }

            int min= 100;

            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(check(places[0][i],places[1][j],places[2][k],places[3][l])){
                                min= Math.min(min,i+j+k+l);
                            }
                        }
                    }
                }
            }

        if(min==100){
            out.append(-1+"\n");
        }
        else{
            out.append(min+"\n");
        }

            }
out.flush();
out.close();


    }

    public static boolean check(Pair p1, Pair p2, Pair p3,Pair p4){
        long d2 = dis(p1, p2); // from p1 to p2
        long d3 = dis(p1, p3); // from p1 to p3
        long d4 = dis(p1, p4); // from p1 to p4

        if (d2 == 0 || d3 == 0 || d4 == 0)
            return false;



        if (d2 == d3 && 2 * d2 == d4
                && 2 * dis(p2, p4) == dis(p2, p3))
        {
            return true;
        }

        // The below two cases are similar to above case
        if (d3 == d4 && 2 * d3 == d2
                && 2 * dis(p3, p2) == dis(p3, p4))
        {
            return true;
        }
        if (d2 == d4 && 2 * d2 == d3
                && 2 * dis(p2, p3) == dis(p2, p4))
        {
            return true;
        }

        return false;














    }


    public static long dis(Pair p1, Pair p2){

        return (p1.x-p2.x)*(p1.x-p2.x) + (p1.y-p2.y)*(p1.y-p2.y);


    }




    public static int localMinUtil(int[] arr, int low,
                                   int high, int n)
    {


        // Find index of middle element
        int mid = low + (high - low) / 2;

        // Compare middle element with its neighbours
        // (if neighbours exist)
        if(mid == 0 || arr[mid - 1] > arr[mid] && mid == n - 1 ||
                arr[mid] < arr[mid + 1])
            return mid;

            // If middle element is not minima and its left
            // neighbour is smaller than it, then left half
            // must have a local minima.
        else if(mid > 0 && arr[mid - 1] < arr[mid])
            return localMinUtil(arr, low, mid - 1, n);

        // If middle element is not minima and its right
        // neighbour is smaller than it, then right half
        // must have a local minima.
        return localMinUtil(arr, mid + 1, high, n);
    }

    // A wrapper over recursive function localMinUtil()
    public static int localMin(int[] arr, int n)
    {
        return localMinUtil(arr, 0, n - 1, n);
    }








    public static String convert(String s,int n){
        if(s.length()==n){
            return s;
        }
        else{
            int x= s.length();
            int v=n-x;
            String str="";
            for (int i = 0; i <v ; i++) {
                str+='0';
            }
            str+=s;
            return str;

        }
    }
    public static int lower(int arr[],int key){
        int low = 0;
        int high = arr.length-1;
        while(low < high){
            int mid = low + (high - low)/2;
            if(arr[mid] >= key){
                high = mid;
            }
            else{
                low = mid+1;
            }
        }
        return low;
    }

    public static int upper(int arr[],int key){
        int low = 0;
        int high = arr.length-1;
        while(low < high){
            int mid = low + (high - low+1)/2;
            if(arr[mid] <= key){
                low = mid;
            }
            else{
                high = mid-1;
            }
        }
        return low;
    }





    static long modExp(long a, long b, long mod) {
        //System.out.println("a is " + a + " and b is " + b);
        if (a==1) return 1;
        long ans = 1;
        while (b!=0) {
            if (b%2==1) {
                ans = (ans*a)%mod;
            }
            a = (a*a)%mod;
            b/=2;
        }
        return ans;
    }


    public static long modmul(long a, long b, long mod) {
        return b == 0 ? 0 : ((modmul(a, b >> 1, mod) << 1) % mod + a * (b & 1)) % mod;
    }

    static long sum(long n){
        //   System.out.println("lol="+ (n*(n-1))/2);
        return (n*(n+1))/2;
    }






    public static ArrayList<Integer> Sieve(int n) {
        boolean arr[]= new boolean [n+1];
        Arrays.fill(arr,true);
        arr[0]=false;
        arr[1]=false;
        for (int i = 2; i*i <=n ; i++) {
            if(arr[i]){
                for (int j = 2; j <=n/i ; j++) {
                    int u= i*j;
                    arr[u]=false;
                }}
        }
        ArrayList<Integer> ans= new ArrayList<>();
        for (int i = 0; i <n+1 ; i++) {
            if(arr[i]){
                ans.add(i);
            }
        }
        return ans;
    }




    static long power( long x, long y, long p)
    {

        long res = 1;


        x = x % p;

        if (x == 0) return 0;

        while (y > 0)
        {

            if((y & 1)==1)
                res = (res * x) % p;


            y = y >> 1;
            x = (x * x) % p;
        }
        return res;
    }

    public static long ceil_div(long a, long b){
        return (a+b-1)/b;
    }

    static long gcd(long a, long b)
    {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    static long lcm(long a, long b)
    {
        return (a*b)/gcd(a, b);
    }

}