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:
//package educational.round01;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;

public class temp {
    InputStream is;
    PrintWriter out;
    String INPUT = "";

    void solve() {
        int n = ni();
        long[][] co = new long[n][];
        for(int i = 0;i < n;i++) {
            co[i] = new long[] {ni(), ni(), i+1};
        }
        Arrays.sort(co, compArgl);

        long bnum = -1;
        long bden = 0;
        int arg = -1;
        for(int i = 0;i < n;i++) {
            int j = (i+1)%n;
            long sig = Long.signum(dot(co[i], co[j]));
            long num = dot(co[i], co[j])*dot(co[i], co[j])*sig;
            long den = dot(co[i], co[i])*dot(co[j], co[j]);

            // bnum*den < num*bden
            if(comp(bnum, bden, num, den) < 0) {
                bnum = num; bden = den;
                arg = i;
            }
        }
        out.println(co[arg][2] + " " + co[(arg+1)%n][2]);
    }

    long comp(long an, long ad, long bn, long bd)
    {
        double bal = (double)an*bd-(double)bn*ad;
        if(Math.abs(bal) > 1e18)return (int)Math.signum(bal);

        return an*bd-bn*ad;
    }

    public static long dot(long[] a, long[] b){ return a[0]*b[0]+a[1]*b[1]; }


    public static Comparator<long[]> compArgl = new Comparator<long[]>(){
        public int compare(long[] a, long[] b) {
            long ax = a[0], ay = a[1];
            long bx = b[0], by = b[1];
            int za = ay > 0 || ay == 0 && ax > 0 ? 0 : 1;
            int zb = by > 0 || by == 0 && bx > 0 ? 0 : 1;
            if(za != zb)return za - zb;
            return Long.signum(ay*bx-ax*by);
        }
    };


    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 temp().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)); }
}