Problem: You are given the set of vectors on the plane, each of them starting at the origin. Your task is to find a pair of vectors with the minimal non-oriented angle between them.

Non-oriented angle is non-negative value, minimal between clockwise and counterclockwise direction angles. Non-oriented angle is always between 0 and π. For example, opposite directions vectors have angle equals to π.

Input

First line of the input contains a single integer n (2 ≤ n ≤ 100 000) — the number of vectors.

The i-th of the following n lines contains two integers xi and yi (|x|, |y| ≤ 10 000, x2 + y2 > 0) — the coordinates of the i-th vector. Vectors are numbered from 1 to n in order of appearing in the input. It is guaranteed that no two vectors in the input share the same direction (but they still can have opposite directions).

Output

Print two integer numbers a and b (a ≠ b) — a pair of indices of vectors with the minimal non-oriented angle. You can print the numbers in any order. If there are many possible answers, print any.

Examples

Input

4
-1 0
0 -1
1 0
1 1


Output

3 4


Input

6
-1 0
0 -1
1 0
1 1
-4 -5
-4 -6


Output

6 5

Solution (in JAVA):

Solution:
import java.util.Arrays;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.math.BigInteger;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Tifuera
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskC solver = new TaskC();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskC {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int n = in.nextInt();

        Vector[] vectors = new Vector[n];
        for (int i = 0; i < n; i++) {
            long x = in.nextInt();
            long y = in.nextInt();

            vectors[i] = new Vector(x, y, i + 1);
        }

        Arrays.sort(vectors);

        Vector first = vectors[0];
        Vector second = vectors[n - 1];

        for (int i = 0; i < n - 1; i++) {
            if (compareAngles(first, second, vectors[i], vectors[i + 1]) > 0) {
                first = vectors[i];
                second = vectors[i + 1];
            }
        }

        out.println(first.vecId + " " + second.vecId);
    }

    private int compareAngles(Vector x1, Vector x2, Vector y1, Vector y2) {
        long prod1 = x1.getProd(x2);
        long prod2 = y1.getProd(y2);

        if (prod1 >= 0 && prod2 < 0) {
            return -1;
        } else if (prod1 < 0 && prod2 >= 0) {
            return 1;
        } else if (prod1 == 0 && prod2 == 0) {
            return 0;
        }

        if (prod1 >= 0) {
            BigInteger prod1BI = BigInteger.valueOf(prod1).pow(2).multiply(BigInteger.valueOf(y1.getSqLen())).multiply(BigInteger.valueOf(y2.getSqLen()));
            BigInteger prod2BI = BigInteger.valueOf(prod2).pow(2).multiply(BigInteger.valueOf(x1.getSqLen())).multiply(BigInteger.valueOf(x2.getSqLen()));
//            prod1 = (prod1 * prod1) * y1.getSqLen() * y2.getSqLen();
//            prod2 = (prod2 * prod2) * x1.getSqLen() * x2.getSqLen();

            return prod2BI.add(prod1BI.negate()).signum();
//            return Long.signum(prod2 - prod1);
        } else {
            BigInteger prod1BI = BigInteger.valueOf(prod1).pow(2).multiply(BigInteger.valueOf(y1.getSqLen())).multiply(BigInteger.valueOf(y2.getSqLen()));
            BigInteger prod2BI = BigInteger.valueOf(prod2).pow(2).multiply(BigInteger.valueOf(x1.getSqLen())).multiply(BigInteger.valueOf(x2.getSqLen()));
//            prod1 = (prod1 * prod1) * y1.getSqLen() * y2.getSqLen();
//            prod2 = (prod2 * prod2) * x1.getSqLen() * x2.getSqLen();

            return prod1BI.add(prod2BI.negate()).signum();
//            return Long.signum(prod1 - prod2);
        }
    }

    private static class Vector implements Comparable<Vector> {
        long x;
        long y;
        int vecId;
        int side;

        public Vector(long x, long y, int vecId) {
            this.x = x;
            this.y = y;
            this.vecId = vecId;

            if (y > 0) {
                side = 0;
            } else if (y < 0) {
                side = 1;
            } else if (x > 0) {
                side = 0;
            } else {
                side = 1;
            }
        }

        private long getProd(Vector other) {
            return x * other.x + y * other.y;
        }

        private long getSqLen() {
            return x * x + y * y;
        }

        private long vecProd(Vector other) {
            return x * other.y - y * other.x;
        }

        public int compareTo(Vector o) {
            if (side != o.side) {
                return Integer.signum(side - o.side);
            }
            return Long.signum(-vecProd(o));
        }
    }

}

class InputReader {
    private BufferedReader reader;
    private String[] currentArray;
    private int curPointer;

    public InputReader(InputStream inputStream) {
        reader = new BufferedReader(new InputStreamReader(inputStream));
    }


    public int nextInt() {
        if ((currentArray == null) || (curPointer >= currentArray.length)) {
            try {
                currentArray = reader.readLine().split(" ");
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            curPointer = 0;
        }
        return Integer.parseInt(currentArray[curPointer++]);
    }

}