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.io.BufferedOutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;


public class ProblemB {

	static class Point {
		int x;
		int y;
		
		public Point(int x, int y) {
			super();
			this.x = x;
			this.y = y;
		}
	}
	
	static class Vector {
		int x;
		int y;
		public Vector(int x, int y) {
			super();
			this.x = x;
			this.y = y;
		}
		
		boolean isMinus(Vector v) {
			return this.x == (v.x * (-1)) && this.y == (v.y * (-1));
		}
		
		boolean isEqual(Vector v) {
			return Math.abs(this.x) == Math.abs(v.y) && Math.abs(this.y) == Math.abs(v.x);
		}
		
		boolean isRightAngle(Vector v) {
			return this.x * v.x + this.y * v.y == 0;
		}
	}
	
	boolean isRectangle(List<Point> points) {
		Vector[] vectors = createVectors(points);
		return isRectangle(vectors);
	}
	
	boolean isRectangle(Vector[] vectors) {
		return vectors[0].isMinus(vectors[2]) && vectors[1].isMinus(vectors[3]) && vectors[0].isRightAngle(vectors[1]); 
	}
	
	boolean isSquare(List<Point> points) {
		Vector[] vectors = createVectors(points);
		return isRectangle(vectors) && vectors[0].isEqual(vectors[1]);
	}
	
	Vector[] createVectors(List<Point> points) {
		points.add(points.get(0));
		Vector[] vectors = new Vector[4];
		Point last = points.get(0);
		for (int i = 1; i < 5; i++) {
			Point curr = points.get(i);
			vectors[i-1] = new Vector(curr.x - last.x, curr.y - last.y);
			last = curr;
		}
		return vectors;
	}
	
	private void solve() throws IOException {
		Scanner stdin = new Scanner(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
        
        Point[] p = new Point[8];
        for (int i = 0; i < 8; i++) {
        	p[i] = new Point(stdin.nextInt(), stdin.nextInt());
        }
        
        boolean[] r = solve(p);
        if (r == null) {
        	out.println("NO");
        } else {
        	out.println("YES");
        	for (int i = 0; i < 8; i++) {
        		if (r[i]) {
        			out.print((i + 1) + " ");
        		}
        	}
        	out.println();
        	for (int i = 0; i < 8; i++) {
        		if (!r[i]) {
        			out.print((i + 1) + " ");
        		}
        	}
        	out.println();
        }
        
        out.flush();
        out.close();
	}
	
	boolean[] solve(Point[] p) {
		for (int mask = 0; mask < (1 << 8); mask++) {
			boolean[] r = new boolean[8];
			int ones = 0;
			for (int i = 0; i < 8; i++) {
				if ((mask & (1 << i)) > 0) {
					ones++;
					r[i] = true;
				}
			}
			if (ones == 4) {
				if (check(r, p)) {
					return r;
				}
			}
		}
		return null;
	}
	
	boolean isSquare(Point[] p) {
		for (int i = 0; i < 4; i++)
			for (int j = 0; j < 4; j++)
				if (j != i) {
					for (int k = 0; k < 4; k++)
						if (k != i && k != j) {
							for (int m = 0; m < 4; m++) {
								if (m != i && m != j && m != k) {
									List<Point> list = new ArrayList<Point>();
									list.add(p[i]);
									list.add(p[j]);
									list.add(p[k]);
									list.add(p[m]);
									if (isSquare(list)) {
										return true;
									}
								}
							}
						}
				}
		
		return false;
	}
	
	boolean isRectangle(Point[] p) {
		for (int i = 0; i < 4; i++)
			for (int j = 0; j < 4; j++)
				if (j != i) {
					for (int k = 0; k < 4; k++)
						if (k != i && k != j) {
							for (int m = 0; m < 4; m++) {
								if (m != i && m != j && m != k) {
									List<Point> list = new ArrayList<Point>();
									list.add(p[i]);
									list.add(p[j]);
									list.add(p[k]);
									list.add(p[m]);
									if (isRectangle(list)) {
										return true;
									}
								}
							}
						}
				}
		
		return false;
	}
	
	private boolean check(boolean[] r, Point[] p) {
		List<Point> squere = new ArrayList<Point>();
		List<Point> rec = new ArrayList<Point>();
		
		for (int i = 0; i < 8; i++) {
			if (r[i]) {
				squere.add(p[i]);
			} else {
				rec.add(p[i]);
			}
		}
		return isSquare(squere.toArray(new Point[0])) && isRectangle(rec.toArray(new Point[0]));
	}

	public static void main(String[] args) throws IOException {
		ProblemB solver = new ProblemB();
        solver.solve();
	}
}