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.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.StringTokenizer;


public class C {

    static StringTokenizer st;
    static BufferedReader br;
    static PrintWriter pw;
    static class Sort implements Comparable<Sort> {
        int x, y, id, quarter;
        public int compareTo(Sort arg0) {
            if (this.quarter > arg0.quarter)
                return 1;
            if (this.quarter < arg0.quarter)
                return -1;
            int x1 = Math.abs(this.x);
            int y1 = Math.abs(this.y);
            int x2 = Math.abs(arg0.x);
            int y2 = Math.abs(arg0.y);
            if (this.quarter==1 || this.quarter==5)
                return y1 * x2 - x1 * y2;
            return -(y1 * x2 - x1 * y2);
        }
    }
    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int n = nextInt();
        Sort[]a = new Sort[n+1];
        for (int i = 1; i <= n; i++) {
            a[i] = new Sort();
            a[i].x = nextInt();
            a[i].y = nextInt();
            a[i].id = i;
            if (a[i].x > 0 && a[i].y==0)
                a[i].quarter = 0;
            else if (a[i].x > 0 && a[i].y > 0)
                a[i].quarter = 1;
            else if (a[i].x==0 && a[i].y > 0)
                a[i].quarter = 2;
            else if (a[i].x < 0 && a[i].y > 0)
                a[i].quarter = 3;
            else if (a[i].x < 0 && a[i].y==0)
                a[i].quarter = 4;
            else if (a[i].x < 0 && a[i].y < 0)
                a[i].quarter = 5;
            else if (a[i].x==0 && a[i].y < 0)
                a[i].quarter = 6;
            else
                a[i].quarter = 7;
        }
        Arrays.sort(a, 1, n+1);
        int i1 = 0, i2 = 0;
        BigInteger nom = BigInteger.valueOf(-(long) 1e18);
        BigInteger denom = BigInteger.valueOf(1);
        for (int i = 1; i <= n; i++) {
            int j = i+1;
            if (i==n)
                j = 1;
            long nom1 = (a[i].x*a[j].x + a[i].y * a[j].y);
            int sign = 1;
            if (nom1 < 0)
                sign = -1;
            nom1 = nom1 * nom1;
            nom1 *= sign;
            long denom1 = (long)(a[i].x*a[i].x+a[i].y*a[i].y) * (a[j].x*a[j].x+a[j].y*a[j].y);
            BigInteger p1 = nom.multiply(BigInteger.valueOf(denom1));
            BigInteger p2 = denom.multiply(BigInteger.valueOf(nom1));
            if (p1.compareTo(p2) < 0) {
                i1 = a[i].id;
                i2 = a[j].id;
                nom = BigInteger.valueOf(nom1);
                denom = BigInteger.valueOf(denom1);
            }
        }
        System.out.println(i1+" "+i2);
        pw.close();
    }
    private static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }
    private static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
    private static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
    private static String next() throws IOException {
        while (st==null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }
}