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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigDecimal;
import java.math.RoundingMode;
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.List;

public class Singleton {
 

    public static void main(String[] args) throws IOException {
        BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));




            String string = bufferedReader.readLine();
            List<Integer> list = new ArrayList<>();
            for (String g : string.split(" ")) {
                list.add(Integer.valueOf(g));
            }
            findNumber(list);




      
    }
    public static BigDecimal findNumber(List<Integer> list){
        BigDecimal bigDecimal1;
        BigDecimal bigDecimal2;
        int skip = 10;

        if (list.get(0) == 0 && list.get(1) == 0 && list.get(2) == 0)  {
            System.out.println("-1");
            return null;
        }
        if (list.get(0) == 0 && list.get(1) == 0 && list.get(2) != 0){
            System.out.println("0");
            return null;
        }
        if (list.get(0) != 0 && list.get(1) == 0 && list.get(2) == 0) {
            System.out.println("1");
            System.out.println("0.000000");

            return null;
        }
        if (list.get(0) == 0 && list.get(1) != 0 && list.get(2) == 0) {
            System.out.println("1");
            System.out.println("0.000000");

            return null;
        }
        if (list.get(0) == 0 && list.get(1) != 0 && list.get(2) != 0){
            bigDecimal1 =new BigDecimal((double)-1 * list.get(2)/list.get(1)).setScale(skip,BigDecimal.ROUND_HALF_UP);
            System.out.println("1");
            System.out.println(bigDecimal1);
            return null;
        }
        if (list.get(0) != 0 && list.get(1) == 0 && list.get(2) != 0){
            if ((list.get(0) > 0 && list.get(2) > 0) || (list.get(0) < 0 && list.get(2) < 0)){
                System.out.println("0");
                return null;
            }
            bigDecimal1 = new BigDecimal(-1 * Math.sqrt((double)-1 * list.get(2)/list.get(0)))
                    .setScale(skip,BigDecimal.ROUND_HALF_UP);
            bigDecimal2 = new BigDecimal( Math.sqrt((double)-1 * list.get(2)/list.get(0)))
                    .setScale(skip,BigDecimal.ROUND_HALF_UP);
            System.out.println("2");
            compar(bigDecimal1,bigDecimal2);
            return null;
        }
        if (list.get(2) == 0 && list.get(1) != 0 && list.get(0) != 0){
            bigDecimal1 =new BigDecimal((double)-1 * list.get(1)/list.get(0)).setScale(skip,BigDecimal.ROUND_UNNECESSARY);
            bigDecimal2 =new BigDecimal(0.0).setScale(skip,BigDecimal.ROUND_HALF_UP);
            System.out.println("2");
            compar(bigDecimal1,bigDecimal2);
            return null;
        }

try{





    long Discrim1 = (long)Math.pow(list.get(1),2) - 4 * (long)list.get(0) * (long)list.get(2);
    if (Discrim1 == 0l){
        System.out.println("1");
        System.out.println(new BigDecimal((-1 * list.get(1)) / (2 * list.get(0))).setScale(skip, BigDecimal.ROUND_HALF_UP));
        return null;
    }
    BigDecimal Discrim = new BigDecimal(Math.sqrt(Math.pow(list.get(1),2) - 4 * list.get(0) *
            list.get(2))).setScale(skip, BigDecimal.ROUND_HALF_UP);
    BigDecimal part1 = new BigDecimal(-1 * list.get(1)).setScale(skip, BigDecimal.ROUND_HALF_UP);
    BigDecimal part2 = new BigDecimal((2 * list.get(0))).setScale(skip, BigDecimal.ROUND_HALF_UP);
    bigDecimal1 = new BigDecimal((part1.doubleValue() + Discrim.doubleValue())/(part2.doubleValue()))
            .setScale(skip, BigDecimal.ROUND_HALF_UP);
    bigDecimal2 = new BigDecimal((part1.doubleValue() - Discrim.doubleValue())/(part2.doubleValue()))
            .setScale(skip, BigDecimal.ROUND_HALF_UP);

    if (bigDecimal1.equals(bigDecimal2)){
        System.out.println("1");
        System.out.println(bigDecimal2);
        return null;
    }
    System.out.println("2");
    compar(bigDecimal1,bigDecimal2);

}catch (NumberFormatException e){
    System.out.println("0");
}
    return null;
    }

    public static void compar(BigDecimal bigDecimal1, BigDecimal bigDecimal2){
        if(bigDecimal2.doubleValue() < bigDecimal1.doubleValue()) {
            System.out.println(bigDecimal2);
            System.out.println(bigDecimal1);
        }else{
            System.out.println(bigDecimal1);
            System.out.println(bigDecimal2);

        }
    }
}