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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;

public class EDUC {

    public static void main(String[] args) throws Exception {
        new EDUC().run();
        out.close();
    }

    long getF(int[] x, int[] y) {
        return x[0] * y[0] + x[1] * y[1];
    }

    long getG(int[] x, int[] y) {
        return (x[0] * x[0] + x[1] * x[1]) * (long) (y[0] * y[0] + y[1] * y[1]);
    }
    
    int comp(long f1, long g1, long f2, long g2) {
        BigInteger f1b = BigInteger.valueOf(f1);
        BigInteger f2b = BigInteger.valueOf(f2);
        BigInteger m1 = f1b.multiply(f1b).multiply(BigInteger.valueOf(f1b.signum())).multiply(BigInteger.valueOf(g2));
        BigInteger m2 = f2b.multiply(f2b).multiply(BigInteger.valueOf(f2b.signum())).multiply(BigInteger.valueOf(g1));
        return m1.compareTo(m2);
    }

    void run() throws Exception {
        int n = nextInt();
        ArrayList<Integer>[] list = new ArrayList[2];
        for (int i = 0; i < 2; ++i) {
            list[i] = new ArrayList<>();
        }
        int[][] coord = new int[n][2];
        int[] one = {1, 0};
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < 2; ++j) {
                coord[i][j] = nextInt();
            }
            if (coord[i][1] >= 0) {
                list[0].add(i);
            } else {
                list[1].add(i);
            }
        }
        for (int i = 0; i < 2; ++i) {
            Collections.sort(list[i], new Comparator<Integer>() {
                @Override
                public int compare(Integer o1, Integer o2) {
                    long f1 = getF(coord[o1], one);
                    long g1 = getG(coord[o1], one);
                    long f2 = getF(coord[o2], one);
                    long g2 = getG(coord[o2], one);
                    return comp(f1, g1, f2, g2);
                }
            });
        }
        for (int i = list[1].size() - 1; i >= 0; --i) {
            list[0].add(list[1].get(i));
        }
        long maxVF = -10000000000l;
        long maxVG = 1;
        int[] id = {0, 1};
        for (int i = 0; i < n; ++i) {
            int j = (i + 1) % n;
            Integer[] v = {list[0].get(i), list[0].get(j)};
            int[] a = new int[]{coord[v[0]][0], coord[v[0]][1]};
            int[] b = new int[]{coord[v[1]][0], coord[v[1]][1]};
            long f = getF(a, b);
            long g = getG(a, b);
            if (comp(f, g, maxVF, maxVG) > 0) {
                maxVF = f;
                maxVG = g;
                id = new int[]{v[0], v[1]};
            }
        }
        out.print((id[0] + 1) + " " + (id[1] + 1));
    }

//~~~~~~~~~~~~~~~~~~~~~~~~~~~ template ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    int[] nextIntArray(int n) throws IOException {
        int[] res = new int[n];
        for (int i = 0; i < n; ++i) {
            res[i] = nextInt();
        }
        return res;
    }

    int[][] nextIntArray(int nx, int ny) throws IOException {
        int[][] res = new int[nx][ny];
        for (int i = 0; i < nx; ++i) {
            for (int j = 0; j < ny; ++j) {
                res[i][j] = nextInt();
            }
        }
        return res;
    }

    long[] nextLongArray(int n) throws IOException {
        long[] res = new long[n];
        for (int i = 0; i < n; ++i) {
            res[i] = nextLong();
        }
        return res;
    }

    long[][] nextLongArray(int nx, int ny) throws IOException {
        long[][] res = new long[nx][ny];
        for (int i = 0; i < nx; ++i) {
            for (int j = 0; j < ny; ++j) {
                res[i][j] = nextLong();
            }
        }
        return res;
    }

    int[][] newIntArray(int nx, int ny, int val) {
        int[][] res = new int[nx][ny];
        for (int i = 0; i < nx; ++i) {
            Arrays.fill(res[i], val);
        }
        return res;
    }

    int[][][] newIntArray(int nx, int ny, int nz, int val) {
        int[][][] res = new int[nx][ny][nz];
        for (int i = 0; i < nx; ++i) {
            for (int j = 0; j < ny; ++j) {
                Arrays.fill(res[i][j], val);
            }
        }
        return res;
    }

    long[][] newLongArray(int nx, int ny, long val) {
        long[][] res = new long[nx][ny];
        for (int i = 0; i < nx; ++i) {
            Arrays.fill(res[i], val);
        }
        return res;
    }

    long[][][] newLongArray(int nx, int ny, int nz, long val) {
        long[][][] res = new long[nx][ny][nz];
        for (int i = 0; i < nx; ++i) {
            for (int j = 0; j < ny; ++j) {
                Arrays.fill(res[i][j], val);
            }
        }
        return res;
    }

    String nextToken() throws IOException {
        while (strTok == null || !strTok.hasMoreTokens()) {
            String line = in.readLine();
            if (line == null) {
                return null;
            }
            strTok = new StringTokenizer(line);
        }
        return strTok.nextToken();
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    static StringTokenizer strTok;
    final static BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    final static PrintWriter out = new PrintWriter(System.out);
}