Problem: You are given an equation: 

Ax2 + Bx + C = 0. 

Your task is to find the number of distinct roots of the equation and print all of them in ascending order.

Input

The first line contains three integer numbers A, B and C ( - 105 ≤ A, B, C ≤ 105). Any coefficient may be equal to 0.

Output

In case of infinite root count print the only integer -1. In case of no roots print the only integer 0. In other cases print the number of root on the first line and the roots on the following lines in the ascending order. Print roots with at least 5 digits after the decimal point.

Examples

Input

1 -5 6


Output

2
2.0000000000
3.0000000000

Solution (in JAVA):

Solution:


import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

import static java.lang.Math.sqrt;

public class Problem20B {

    public static void main(String[] args) {
        Problem20B problem20b = new Problem20B();
        problem20b.inputParams.readInputParamsFromStream();
        problem20b.solve();
        problem20b.outputParams.writeOutputParamsToStream();
    }

    public long a, b, c;
    public long rootNum;
    public double ad, bd, cd, x1, x2;

    public class InputParams extends AbstractInputParams {
        @Override
        public void readInputParamsFromStream() {
            a = readInteger();
            b = readInteger();
            c = readInteger();
        }
    }

    public class OutputParams extends AbstractOutputParams {
        @Override
        public void writeOutputParamsToStream() {
            switch ((int) rootNum) {
                case -1:
                case 0:
                    writeInteger(rootNum);
                    break;

                case 1:
                    writeInteger(rootNum);
                    writeDouble(x1);
                    break;

                case 2:
                    writeInteger(rootNum);
                    writeDouble(x1);
                    writeDouble(x2);
                    break;
            }
        }
    }

    // Problem solution implementation
    public void solve() {

        ad = a;
        bd = b;
        cd = c;

        if (ad == 0 && bd == 0 && cd == 0) {
            rootNum = -1;
            return;
        }

        if (ad == 0 && bd == 0 && cd != 0) {
            rootNum = 0;
            return;
        }

        if (ad == 0) {
            rootNum = 1;
            x1 = -cd / bd;
            return;
        }

        double d = bd * bd - 4 * ad * cd;

        if (d < 0) {
            rootNum = 0;
            return;
        }

        if (d == 0) {
            rootNum = 1;
            x1 = -bd / (2 * ad);
            return;
        }

        if (d > 0) {
            rootNum = 2;
            double rootD = sqrt(d);

            List<Double> dList = new ArrayList<Double>();
            dList.add((-bd - rootD) / (2 * ad));
            dList.add((-bd + rootD) / (2 * ad));
            Collections.sort(dList);

            x1 = dList.get(0);
            x2 = dList.get(1);
            return;
        }

        throw (new IllegalArgumentException());
    }


    //Problem input/output classes

    abstract class AbstractInputParams {
        abstract public void readInputParamsFromStream();

        protected Scanner inputScanner = new Scanner(System.in);

        protected Long readInteger() {
            if (inputScanner.hasNextLong()) {
                return inputScanner.nextLong();
            } else {
                throw new IllegalArgumentException();
            }
        }

        protected List<String> readStringList(Long length) {
            List<String> stringList = new ArrayList<String>();
            for (int i = 0; i < length; i++) {
                String string = readString();
                stringList.add(string);
            }
            return stringList;
        }


        protected List<Long> readIntegerList(Long length) {
            List<Long> integerList = new ArrayList<Long>();
            for (int i = 0; i < length; i++) {
                Long integerValue = readInteger();
                integerList.add(integerValue);
            }
            return integerList;
        }


        protected String readString() {
            return inputScanner.next();
        }

    }

    abstract class AbstractOutputParams {
        abstract public void writeOutputParamsToStream();

        void writeInteger(Long i) {
            System.out.print(i);
            System.out.print(" ");
        }

        void writeString(String string) {
            System.out.print(string);
            System.out.print(" ");
        }

        void writeStringList(List<String> stringList) {
            for (String string : stringList) {
                writeString(string);
            }
        }

        void writeDouble(double f) {
            System.out.print(f);
            System.out.print(" ");
        }

    }

    InputParams inputParams = new InputParams();
    OutputParams outputParams = new OutputParams();
}