Problem: There are N holes in a two-dimensional plane. The coordinates of the i-th hole are (x_i,y_i).

Let R=10^{10^{10^{10}}}. Ringo performs the following operation:

* Randomly choose a point from the interior of a circle of radius R centered at the origin, and put Snuke there. Snuke will move to the hole with the smallest Euclidean distance from the point, and fall into that hole. If there are multiple such holes, the hole with the smallest index will be chosen.



For every i (1 \leq i \leq N), find the probability that Snuke falls into the i-th hole.

Here, the operation of randomly choosing a point from the interior of a circle of radius R is defined as follows:

* Pick two real numbers x and y independently according to uniform distribution on [-R,R].
* If x^2+y^2\leq R^2, the point (x,y) is chosen. Otherwise, repeat picking the real numbers x,y until the condition is met.

Constraints

* 2 \leq N \leq 100
* |x_i|,|y_i| \leq 10^6(1\leq i\leq N)
* All given points are pairwise distinct.
* All input values are integers.

Input

Input is given from Standard Input in the following format:


N
x_1 y_1
:
x_N y_N


Output

Print N real numbers. The i-th real number must represent the probability that Snuke falls into the i-th hole.

The output will be judged correct when, for all output values, the absolute or relative error is at most 10^{-5}.

Examples

Input

2
0 0
1 1


Output

0.5
0.5


Input

5
0 0
2 8
4 5
2 6
3 10


Output

0.43160120892732328768
0.03480224363653196956
0.13880483535586193855
0.00000000000000000000
0.39479171208028279727

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.Reader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.TreeMap;
import java.io.BufferedReader;
import java.util.Collections;
import java.io.InputStream;

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

    static class TaskB {
        public void solve(int testNumber, MyInput in, PrintWriter out) {
            int n = in.nextInt();

            List<Point> p = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                int x = in.nextInt();
                int y = in.nextInt();
                p.add(new Point(x, y, i));
            }
            List<Point> q = GenConvexHull(p);
            TreeMap<Point, Integer> set = new TreeMap<>();
            for (int i = 0; i < q.size(); i++) {
                set.put(q.get(i), i);
            }
//        dump(q);
            for (int ii = 0; ii < p.size(); ii++) {
                if (!set.containsKey(p.get(ii))) {
                    out.printf("%.10f\n", 0.0);
                    continue;
                }

                int i = set.get(p.get(ii));
                int j = (i + q.size() - 1) % q.size();
                int k = (i + 1) % q.size();

                double a1 = angle(q.get(j), q.get(i));
                double a2 = angle(q.get(i), q.get(k));
                double a = a1 - a2;
                if (a < 0) a += 2 * Math.PI;
//            dump(a1*180/Math.PI, a2*180/Math.PI, q.get(i), q.get(j), q.get(k));
                out.printf("%.10f\n", a / (2 * Math.PI));
            }
        }

        double angle(Point a, Point b) {
            Point d = a.sub(b);
            return Math.atan2(d.y, d.x);
        }

        private static boolean LeftRotate(List<Point> ps, int len) {
            int i = len - 2;
            double x1 = ps.get(i - 1).x, x2 = ps.get(i).x, x3 = ps.get(i + 1).x,
                    y1 = ps.get(i - 1).y, y2 = ps.get(i).y, y3 = ps.get(i + 1).y;
            Double cp = (x2 - x1) * (y3 - y1) - (y2 - y1) * (x3 - x1);
            return cp >= 0;
        }

        static List<Point> GenConvexHull(List<Point> pss) {
            if (pss.size() < 3) return pss;

            List<Point> ps = new ArrayList<>(pss);
            Collections.sort(ps);
            int ul = 0;
            final List<Point> upper = new ArrayList<Point>(ps.size());
            for (int i = 0; i < ps.size(); i++) {
                upper.add(null);
            }

            upper.set(ul++, ps.get(0));
            upper.set(ul++, ps.get(1));
            for (int i = 2; i < ps.size(); i++) {
                upper.set(ul++, ps.get(i));
                while (ul >= 3 && LeftRotate(upper, ul)) {
                    upper.set(ul - 2, upper.get(ul - 1));
                    ul--;
                }
            }

            int ll = 0;
            final List<Point> lower = new ArrayList<Point>(ps.size());
            for (int i = 0; i < ps.size(); i++) {
                lower.add(null);
            }

            lower.set(ll++, ps.get(ps.size() - 1));
            lower.set(ll++, ps.get(ps.size() - 2));
            for (int i = ps.size() - 3; i >= 0; i--) {
                lower.set(ll++, ps.get(i));
                while (ll >= 3 && LeftRotate(lower, ll)) {
                    lower.set(ll - 2, lower.get(ll - 1));
                    ll--;
                }
            }

            final List<Point> res = new ArrayList<Point>(ul + ll - 2);
            for (int i = 0; i < ul - 1; i++) res.add(upper.get(i));
            for (int i = 0; i < ll - 1; i++) res.add(lower.get(i));
            return res;
        }

        public class Point implements Comparable<Point> {
            public double x;
            public double y;
            int idx;

            public Point() {
            }

            public Point(double xx, double yy, int idx) {
                x = xx;
                y = yy;
                this.idx = idx;
            }

            public Point(Point p) {
                this(p.x, p.y, p.idx);
            }

            public Point subM(double x, double y) {
                this.x -= x;
                this.y -= y;
                return this;
            }

            public Point sub(Point p) {
                return sub(p.x, p.y);
            }

            public Point sub(double x, double y) {
                return new Point(this).subM(x, y);
            }

            public String toString() {
                return "(" + x + "," + y + ")";
            }


            public int compareTo(Point o) {
                final int cmp = Double.compare(x, o.x);
                return cmp != 0 ? cmp : Double.compare(y, o.y);
            }

        }

    }

    static class MyInput {
        private final BufferedReader in;
        private static int pos;
        private static int readLen;
        private static final char[] buffer = new char[1024 * 8];
        private static char[] str = new char[500 * 8 * 2];
        private static boolean[] isDigit = new boolean[256];
        private static boolean[] isSpace = new boolean[256];
        private static boolean[] isLineSep = new boolean[256];

        static {
            for (int i = 0; i < 10; i++) {
                isDigit['0' + i] = true;
            }
            isDigit['-'] = true;
            isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
            isLineSep['\r'] = isLineSep['\n'] = true;
        }

        public MyInput(InputStream is) {
            in = new BufferedReader(new InputStreamReader(is));
        }

        public int read() {
            if (pos >= readLen) {
                pos = 0;
                try {
                    readLen = in.read(buffer);
                } catch (IOException e) {
                    throw new RuntimeException();
                }
                if (readLen <= 0) {
                    throw new MyInput.EndOfFileRuntimeException();
                }
            }
            return buffer[pos++];
        }

        public int nextInt() {
            int len = 0;
            str[len++] = nextChar();
            len = reads(len, isSpace);
            int i = 0;
            int ret = 0;
            if (str[0] == '-') {
                i = 1;
            }
            for (; i < len; i++) ret = ret * 10 + str[i] - '0';
            if (str[0] == '-') {
                ret = -ret;
            }
            return ret;
        }

        public char nextChar() {
            while (true) {
                final int c = read();
                if (!isSpace[c]) {
                    return (char) c;
                }
            }
        }

        int reads(int len, boolean[] accept) {
            try {
                while (true) {
                    final int c = read();
                    if (accept[c]) {
                        break;
                    }
                    if (str.length == len) {
                        char[] rep = new char[str.length * 3 / 2];
                        System.arraycopy(str, 0, rep, 0, str.length);
                        str = rep;
                    }
                    str[len++] = (char) c;
                }
            } catch (MyInput.EndOfFileRuntimeException e) {
            }
            return len;
        }

        static class EndOfFileRuntimeException extends RuntimeException {
        }

    }
}