Problem: Little Petya very much likes rectangles and especially squares. Recently he has received 8 points on the plane as a gift from his mother. The points are pairwise distinct. Petya decided to split them into two sets each containing 4 points so that the points from the first set lay at the vertexes of some square and the points from the second set lay at the vertexes of a rectangle. Each point of initial 8 should belong to exactly one set. It is acceptable for a rectangle from the second set was also a square. If there are several partitions, Petya will be satisfied by any of them. Help him find such partition. Note that the rectangle and the square from the partition should have non-zero areas. The sides of the figures do not have to be parallel to the coordinate axes, though it might be the case.

Input

You are given 8 pairs of integers, a pair per line — the coordinates of the points Petya has. The absolute value of all coordinates does not exceed 104. It is guaranteed that no two points coincide.

Output

Print in the first output line "YES" (without the quotes), if the desired partition exists. In the second line output 4 space-separated numbers — point indexes from the input, which lie at the vertexes of the square. The points are numbered starting from 1. The numbers can be printed in any order. In the third line print the indexes of points lying at the vertexes of a rectangle in the similar format. All printed numbers should be pairwise distinct.

If the required partition does not exist, the first line should contain the word "NO" (without the quotes), after which no output is needed.

Examples

Input

0 0
10 11
10 0
0 11
1 1
2 2
2 1
1 2


Output

YES
5 6 7 8
1 2 3 4


Input

0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7


Output

NO


Input

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


Output

YES
1 2 3 4
5 6 7 8

Note

Pay attention to the third example: the figures do not necessarily have to be parallel to the coordinate axes.

Solution (in JAVA):

Solution:
import java.awt.geom.Line2D;
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.InputStreamReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;



public class C97P4 {

    private static BufferedReader in;
    private static PrintWriter out;
    private static StringTokenizer input;
    
    static int [] x = new int[9];
    static int [] y = new int[9];
    public static void main(String[] args) throws IOException {
        //-------------------------------------------------------------------------
        //Initializing...
        new C97P4();
        //-------------------------------------------------------------------------
        //put your code here... :)
        for (int i = 1; i < 9; i++) {
            x[i]=nextInt();
            y[i]=nextInt();
        }
        boolean c = can(0);
        if(c){
            writeln("YES");
            for (int j = 0; j < 4; j++) {
                write(perm[j]+((j+1==4)?"\n":" "));
            }
            for (int j = 4; j < 8; j++) {
                
                write(perm[j]+((j+1==8)?"\n":" "));
            }
        }else
        writeln("NO");
        //-------------------------------------------------------------------------
        //closing up
        end();
        //--------------------------------------------------------------------------

    }
    
    static int [] perm = new int[8];
    static boolean [] vis =new boolean[9]; 
    static boolean can(int l){
        if(l==8)return check();
        boolean res=false;
        for (int i = 1; i < 9; i++) {
            if(!vis[i]){
                vis[i]=true;
                perm[l]=i;
                res|=can(l+1);
                if(res)return true;;
                vis[i]=false;
            }
        }
        return res;
    }
    
    
    private static boolean check() {
        // TODO Auto-generated method stub
        for (int i = 0; i < 4; i++) {
            if(!angle90s(perm[i],perm[ (i+1)%4], perm[(i+2)%4]))return false;
        }
        for (int i = 4; i < 8; i++) {
            if(!angle90(perm[i], perm[(i+1==8)?4:i+1], perm[(i+2==9)?5:(i+2==8)?4:i+2]))return false;
        }
        return true;
    }
    private static boolean angle90s(int i , int j , int k){
        int aa = (x[i]-x[j])*(x[i]-x[j])+(y[i]-y[j])*(y[i]-y[j]);
        int bb = (x[j]-x[k])*(x[j]-x[k])+(y[j]-y[k])*(y[j]-y[k]);
        int cc = (x[i]-x[k])*(x[i]-x[k])+(y[i]-y[k])*(y[i]-y[k]);
        return aa+bb==cc&&aa==bb;
    }
    private static boolean angle90(int i , int j , int k){
        int aa = (x[i]-x[j])*(x[i]-x[j])+(y[i]-y[j])*(y[i]-y[j]);
        int bb = (x[j]-x[k])*(x[j]-x[k])+(y[j]-y[k])*(y[j]-y[k]);
        int cc = (x[i]-x[k])*(x[i]-x[k])+(y[i]-y[k])*(y[i]-y[k]);
        return aa+bb==cc;
    }

    


    public C97P4() throws IOException {
        //Input Output for Console to be used for trying the test samples of the problem 
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        //-------------------------------------------------------------------------
        //Initalize Stringtokenizer input
        input = new StringTokenizer(in.readLine());
    }

    private static int nextInt() throws IOException {
        if (!input.hasMoreTokens())input=new StringTokenizer(in.readLine());
        return Integer.parseInt(input.nextToken());
    }
    private static long nextLong() throws IOException {
        if (!input.hasMoreTokens())input=new StringTokenizer(in.readLine());
        return Long.parseLong(input.nextToken());
    }
    private static double nextDouble() throws IOException {
        if (!input.hasMoreTokens())input=new StringTokenizer(in.readLine());
        return Double.parseDouble(input.nextToken());
    }
    private static String nextString() throws IOException {
        if (!input.hasMoreTokens())input=new StringTokenizer(in.readLine());
        return input.nextToken();
    }
    private static void write(String output){
        out.write(output);
        out.flush();
    }
    private static void writeln(String output){
        out.write(output+"\n");
        out.flush();
    }
    private static void end() throws IOException{
        in.close();
        out.close();
        System.exit(0);
    }

    

}