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.
//package round271;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class C {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		for(int T = ni();T >= 1;T--){
			int[][] co = new int[4][];
			for(int i = 0;i < 4;i++){
				co[i] = na(4);
			}
			int min = 999;
			for(int a = 0;a < 4;a++){
				for(int b = 0;b < 4;b++){
					for(int c = 0;c < 4;c++){
						for(int d = 0;d < 4;d++){
							if(issq(co)){
								min = Math.min(min, a+b+c+d);
							}
							rot(co[3]);
						}
						rot(co[2]);
					}
					rot(co[1]);
				}
				rot(co[0]);
			}
			out.println(min == 999 ? -1 : min);
		}
	}
	
	boolean issq(int[][] co)
	{
		int[] ord = new int[4];
		for(int i = 0;i < 4;i++)ord[i] = i;
		do{
			if(isSq(
					co[ord[0]][0], co[ord[0]][1],
					co[ord[1]][0], co[ord[1]][1],
					co[ord[2]][0], co[ord[2]][1],
					co[ord[3]][0], co[ord[3]][1]
							)){
				return true;
			}
		}while(nextPermutation(ord));
		return false;
	}
	
	static boolean nextPermutation(int[] src) {
		int i;
		for (i = src.length - 2; i >= 0 && src[i] > src[i + 1]; i--)
			;
		if (i == -1)
			return false;
		int j;
		for (j = i + 1; j < src.length && src[i] < src[j]; j++)
			;
		int d = src[i];
		src[i] = src[j - 1];
		src[j - 1] = d;
		for (int p = i + 1, q = src.length - 1; p < q; p++, q--) {
			d = src[p];
			src[p] = src[q];
			src[q] = d;
		}
		return true;
	}
	
	public static boolean isSq(int ax, int ay, int bx, int by, int cx, int cy, int dx, int dy)
	{
		int vx = bx-ax;
		int vy = by-ay;
		return (!(dx == ax && dy == ay) && cx == ax + vy && cy == ay - vx && dx == bx + vy && dy == by - vx);
	}
	
	void rot(int[] c)
	{
		int x = c[0], y = c[1];
		int a = c[2], b = c[3];
		int nx = -(y-b)+a;
		int ny = (x-a)+b;
		c[0] = nx; c[1] = ny;
	}
	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new C().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}
