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.*;
import java.io.*;
import java.math.BigInteger;
import java.util.regex.Pattern;
import javafx.util.Pair;
import sun.util.locale.StringTokenIterator;

public class Foh {

    static BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
    static StringBuilder out = new StringBuilder();
    static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
    static PrintWriter pw = new PrintWriter(new OutputStreamWriter(System.out));

    static int I(String s) {
        return Integer.parseInt(s);
    }

    static long L(String s) {
        return Long.parseLong(s);
    }

    static double D(String s) {
        return Double.parseDouble(s);
    }

    static String[] SA() throws IOException {
        return bf.readLine().split(" ");
    }

    public static void main(String[] args) throws IOException {

        /*    int n = I(bf.readLine());
        ArrayList<Integer> al = new ArrayList();

        HashMap hm = new HashMap();
        StringTokenizer in = new StringTokenizer(bf.readLine());

        for (int i = 0; i < n; i++) {
            int x = I(in.nextToken());
            al.add(x);
        }
        int let = 0;
        int inc = 0;
        int max = 0;
        for (int i = 0; i < n; i++) {
            int x = al.get(i);
            if (!hm.containsKey(x)) {
                hm.put(x, 0);
                inc++;
            } else {
                if (let > 0) {
                    max = Math.max(max, inc);
                    inc = 1;
                    hm = new HashMap();
                    hm.put(x, 0);
                } else {
                    let = 1;
                    for (int j = i + 1; j < n; j++) {
                        if (!hm.containsKey(al.get(j))) {
                            i = j - 1;
                            break;
                        }
                    }
                }
            }
        }
        System.out.println(n-Math.max(max, inc));*/
 /*  StringBuffer st = new StringBuffer();
        st.append(bf.readLine());
        int x = 0;
        int num = -1;
        boolean key=false;
        int str=0;
        for (int i = 0; i < st.length(); i++) {
            
            if ((st.charAt(i) - '0') % 2 == 0 && (st.charAt(i) - '0') < st.charAt(st.length()-1)-'0') {
                num = (st.charAt(i) - '0');
                x = i;break;
            }

        }
        if(num==-1){
         for (int i = st.length()-1; i >=0; i--) {
            
            if ((st.charAt(i) - '0') % 2 == 0 ) {
                num = (st.charAt(i) - '0');
                x = i;break;
            }

        }
        }
        for (int i = 0; i < st.length(); i++) {
            
          if(st.charAt(i)=='0'&&!key){str=i+1;}else{key=true;break;}

        }
        if (num != -1) {
            st.setCharAt(x, st.charAt(st.length() - 1));
            st.setCharAt(st.length()-1, (char)(num+'0'));
            System.out.println(st.substring(str));
        } else {
            System.out.println("-1");
        }*/
 /*  StringTokenizer in = new StringTokenizer(bf.readLine());
        int n = I(in.nextToken());
        int k = I(in.nextToken());
        if(n==k){n--;}
        in = new StringTokenizer(bf.readLine());
int numco=0;
        HashMap<Integer, Integer> hm = new HashMap();
        ArrayList<Integer> al = new ArrayList();
        for (int i = 0; i < Math.min(k, n); i++) {
            int x = I(in.nextToken());
          
                al.add(x);
               if(!hm.containsKey(x)){
                   numco++;
                   hm.put(x, x);
               }

        }
     if(numco==k){k--;}
       int inc=0;
      hm = new HashMap();
        for (int i = 0; i <al.size(); i++) {
            int x=al.get(i);
            if(!hm.containsKey(x)){
            inc++;
            hm.put(x, x);
            out.insert(0, al.get(i)+" ");
        }if(inc==k)break;}
        System.out.print(inc+"\n"+out);*/
 /*   StringTokenizer in = new StringTokenizer(bf.readLine());
        int n = I(in.nextToken());
        int k = I(in.nextToken());
        ArrayList<Integer> al = new ArrayList();
        in = new StringTokenizer(bf.readLine());
        int prev = I(in.nextToken());

        for (int i = 1; i < n; i++) {
int x=I(in.nextToken());
al.add(x-prev);
prev=x;        }
        Collections.sort(al);
        int sum=0;
        for(int i=0;i<n-k;i++){sum+=al.get(i);}
        System.out.println(sum);*/
 /*  int n = I(bf.readLine());
        String st = bf.readLine();
        ArrayList<Integer> al = new ArrayList();
        StringTokenizer in = new StringTokenizer(bf.readLine());
        for (int i = 0; i < 9; i++) {
            al.add(I(in.nextToken()));
        }
        int x=0;
        int ind=0;
        for (int i = 0; i < st.length(); i++) {
            if(al.get(st.charAt(i)-'0')>(st.charAt(i)-'0')){
                ind=st.charAt(i)-'0';
            x=i;break;
            }
        }
        int inc=0;
        for(int i=x;i>=0;i--){
        
        }
        System.out.println(out);*/
 /*     int t = I(bf.readLine());
        while (t-- > 0) {
            StringTokenizer in = new StringTokenizer(bf.readLine());
            int n = I(in.nextToken());
            int x = I(in.nextToken());
            int min = Integer.MAX_VALUE;
            boolean tf = false;
            for (int i = 0; i < n; i++) {
                in = new StringTokenizer(bf.readLine());
                int d = I(in.nextToken());
                int h = I(in.nextToken());
                 if(d>=x&&!tf){tf=true;min=1;}
          else if(!tf&&d>h){
                  
                if((d-h)>=Math.ceil(x/2.0)){min=2;}
                else{
                int te=x/(d-h);
                if(x%(d-h)!=0){
              //      System.out.println((te*d)-((te-1)*d)<x);
                if((te*d)-((te-1)*h)<x){te++;}
                
                
                }
                min=Math.min(min,te);
                }
                }
            }
            if (min == Integer.MAX_VALUE) {
                min = -1;
            }
            System.out.println(min);
        }*/
 /* StringTokenizer in = new StringTokenizer(bf.readLine());
        int n = I(in.nextToken());
 
        int q = I(in.nextToken());
        int a[][] = new int[3][n + 9];
        
        ArrayList<HashSet<Integer>> al = new ArrayList();
        for (int i = 0; i < 3; i++) {
            al.add(new HashSet<Integer>());
        }
 
        while (q-- > 0) {
            in = new StringTokenizer(bf.readLine());
            int r = I(in.nextToken());
            int c = I(in.nextToken()) + 3;
            a[r][c] = a[r][c] == 1 ? 0 : 1;
           if(r==1){
           if(a[r][c]==1&&(a[2][c]==1||a[2][c+1]==1||a[2][c-1]==1)){inc++;}
           else if(a[r][c]==0&&(a[2][c]==1||a[2][c+1]==1||a[2][c-1]==1)){if(inc>0)inc--;}}
           else {
               if (a[r][c] == 0) {
                   tester(c, a);
               } else if (a[r][c] == 1) {
                   tester1(c, a);
               }
           }
            System.out.println(inc);
            if(inc==0){out.append("YeS\n");}else{out.append("nO\n");}
        }
        System.out.print(out);*/
 /*int t = I(bf.readLine());
for(int i=0;i<26;i++){al1[i]=new HashSet();}
boolean  check[]=new boolean[26];
        for (int i = 0; i < t; i++) {

            String n = bf.readLine();
            ArrayList<Integer> al = new ArrayList();
            HashSet<Integer> set = new HashSet();
            for (int j = 0; j < n.length(); j++) {
                int x = n.charAt(j) - 'a';
                if (!set.contains(x)) {check[x]=true;
                    set.add(x);
                    al.add(x);
                }

            }
            for (int j = 1; j < al.size(); j++) {
                al1[al.get(j)].add(al.get(j - 1));
                al1[al.get(j - 1)].add(al.get(j));
            }
        }
        for (int i = 0; i < 26; i++) {
            if (!id[i]&&check[i]) {
                inc++;
                dfs(i);
            }
        }
        System.out.println(inc);*/
 /*  int t = I(bf.readLine());
        while (t-- > 0) {
            StringTokenizer in = new StringTokenizer(bf.readLine());
            int n = I(in.nextToken());
            int k = I(in.nextToken());
            String st = bf.readLine();
            int str = st.indexOf("1");
            int end = st.lastIndexOf("1");
            if (str == end) {
                out.append("0\n");
            } else {
                int dp[] = new int[st.length()];
                int sum = 0;
                for (int i = 0; i < st.length(); i++) {
                    if (st.charAt(i) == '1') {
                        sum++;
                    }
                    dp[i] = sum;
                }
                int a[][] = new int[2][st.length()];
                int min = Integer.MAX_VALUE;
                for (int i = str; i <= Math.min(str + k, end); i++) {
                    int inc = 0;
                    int var = i + k;
                    while (true) {

                        if (var >= end) {
                            System.out.println(dp[end - 1] + "  " + dp[var - k] + "    " + (end - 1) + "  " + (var - k) + "   " + var);
                            inc += (dp[end - 1] - dp[var - k]);

                            break;
                        }
                        System.out.println((var - 1) + "   " + (var - k) + "   " + var);
                        //   inc += dp[var -1] - ((var - k)!=0?dp[var - k]:0);

                        inc += dp[var - 1] - dp[var - k];
                        if (st.charAt(var) == '0') {
                            inc++;
                        }
                        var += k;

                    }
                    System.out.println("inc1:"+inc);
                  if(i!=0)  inc+=(dp[i-1]);
                    System.out.println("inc2:"+inc);
                    //   min=Math.min(inc,min);
                }
                //System.out.println(min);
            }
        }
        System.out.println(out);*/
        //B-
        /*
       int t = I(bf.readLine());
        while (t-- > 0) {
             int n = I(bf.readLine());
            StringTokenizer in = new StringTokenizer(bf.readLine());
           ArrayList<Integer> al=new ArrayList();
            for(int i=0;i<n;i++){al.add(I(in.nextToken()));}
            Collections.sort(al);
            int min=Integer.MAX_VALUE;
            for(int i=1;i<n;i++){ min=Math.min(min,al.get(i)-al.get(i-1));}
            out.append(min+"\n");
        }
        System.out.println(out);*/
        //c-
        /*
       int t = I(bf.readLine());
        while (t-- > 0) {
             int n = I(bf.readLine());
            StringTokenizer in = new StringTokenizer(bf.readLine());
            int o=0;
            int e=0;
            ArrayList<Integer> al=new ArrayList();
            HashMap<Integer,Integer> hm=new HashMap();
            for(int i=0;i<n;i++){
            int x=I(in.nextToken());
            if(x%2==0){al.add(x);e++;}else{hm.put(x, 0);o++;}
            
            }
            if(o%2==0&&e%2==0){out.append("YES\n");}
            else{
                boolean tf=false;
            for(int i=0;i<al.size();i++){
            if(hm.containsKey(al.get(i)-1)||hm.containsKey(al.get(i)+1)){tf=true;break;}
            }
            if(tf){out.append("YES\n");}
            else{out.append("NO\n");}
            }
        }System.out.println(out);*/
        //D
        /*
        int t = I(bf.readLine());
        while (t-- > 0) {

            StringTokenizer in = new StringTokenizer(bf.readLine());
            int n = I(in.nextToken());
            int k = I(in.nextToken());
            ArrayList<Integer> al = new ArrayList();
            for (int i = 1; i * i <= n ; i++) {
                if (n % i == 0) {
                    al.add(i);
                    al.add(n/i);
                }
            }
            al.add(n);
            Collections.sort(al);
            for (int i = al.size() - 1; i >= 0; i--) {
                if (al.get(i) <= k) {
                    out.append((n/al.get(i)) + "\n");break;
                }
            }
        }
        System.out.println(out);
         */
        //A
        /*
           int t = I(bf.readLine());
        while (t-- > 0) {

            StringTokenizer in = new StringTokenizer(bf.readLine());
            int n = I(in.nextToken());
            int k = I(in.nextToken());
        int x=n*k;
        int min=Integer.MAX_VALUE;
        if(n*2>=k){min=Math.min(min, n*2);}
        if(n<=k*2){min=Math.min(min, k*2);}
          if(n>=k*2){min=Math.min(min, n);}
        if(n*2<=k){min=Math.min(min, k);}
      min=Math.min(min, n+k);
     
    //        System.out.println(min);
        int i=1;
       while(true){
        if(i*i>=(2*x)&&(i>=min)){out.append((i*i)+"\n");break;}
        i++;
        }
        
        }
        System.out.println(out);
    
         */
 /*  int t = I(bf.readLine());
        while (t-- > 0) {
            int n = I(bf.readLine());
            char a[][]=new char[n][];
            for(int i=0;i<n;i++){a[i]=bf.readLine().toCharArray();}
            boolean[][] tf=new boolean[n][n];
            for(int i=0;i<n;i++){
            
                for(int j=n-1;j>=0;j--){
                if(a[i][j]=='1'){tf[i][j]=true;}else{break;}
                }
            for(int j=n-1;j>=0;j--){
                if(a[j][i]=='1'){tf[j][i]=true;}else{break;}
                }
            }
            boolean isok=false;
            for(int i=n-2;i>=0;i--){
            
            for(int j=n-2;j>=0;j--){
            if(!tf[i][j]&&a[i][j]=='1'){
            if(tf[i+1][j]||tf[i][j+1]){tf[i][j]=true;}
            else{isok=true;break;}
            }
            
            }
            }
            if(isok){out.append("NO\n");}else{out.append("YES\n");}
        }
        System.out.println(out);*/
        StringTokenizer in = new StringTokenizer(bf.readLine());
        long a = I(in.nextToken());
        long b = I(in.nextToken());
        long c = I(in.nextToken());
        if (a == 0 && b == 0&&c==0) {
            System.out.println("-1");
        } else  if (a == 0 && b == 0&&c!=0) {
            System.out.println("0");
        } else if (a == 0 && b != 0) {
            System.out.println("1");
            System.out.printf("%.5f%n", ((-c * 1.0) / (b * 1.0)));
        } else if (b == 0 && a != 0) {

            if ((a < 0 && c >= 0) || (c <= 0 && a > 0)) {
                if (Math.sqrt((-c * 1.0) / (a * 1.0)) != 0) {
                    System.out.println("2");
                    System.out.printf("%.5f%n", -Math.sqrt((-c * 1.0) / (a * 1.0)));
                    System.out.printf("%.5f%n", Math.sqrt((-c * 1.0) / (a * 1.0)));
                } else {
                    System.out.println("1");
                    System.out.printf("%.5f%n", Math.sqrt((-c * 1.0) / (a * 1.0)));
                }
            } else {
                System.out.println("0");
            }
        } else {

            if ((b * b) - (4 * a * c) < 0) {
                System.out.println(0);
            } else if ((b * b) - (4 * a * c) == 0) {
                System.out.println("1");
                System.out.printf("%.5f%n", ((-b * 1.0) / (2 * a * 1.0)));
            } else {

                
                double max = Math.max(((((-b) * 1.0) + Math.sqrt((b * 1.0 * b * 1.0) - (4.0 * a * 1.0 * c * 1.0))) / (2.0 * a)), (((-b) - Math.sqrt((b * 1.0 * b * 1.0) - (4.0 * a * 1.0 * c * 1.0))) / (2.0 * a)));
                double min = Math.min(((((-b) * 1.0) + Math.sqrt((b * 1.0 * b * 1.0) - (4.0 * a * 1.0 * c * 1.0))) / (2.0 * a)), (((-b) - Math.sqrt((b * 1.0 * b * 1.0) - (4.0 * a * 1.0 * c * 1.0))) / (2.0 * a)));
                if ((min == 0 && max == min)) {
                    System.out.println("1\n");
                    System.out.print("0.000000");

                }
                else{
                    System.out.println("2\n");
                    System.out.printf("%.5f%n", (min));

                    System.out.printf("%.5f%n", (max));
                }
            }
        }
    }
    /*
    1
9 2
100100100

     */

    static boolean id[] = new boolean[26];
    static HashSet<Integer> al1[] = new HashSet[26];

    static void dfs(int i) {
        id[i] = true;
        for (Integer x : al1[i]) {
            if (!id[x]) {
                dfs(x);
            }
        }
    }
    static int inc = 0;

    static void tester(int x, int a[][]) {
        if (a[1][x] == 1 && a[2][x + 1] == 0 && a[2][x - 1] == 0 && a[2][x] == 0) {
            if (inc > 0) {
                inc--;
            }
        }
        if (a[1][x + 1] == 1 && a[2][x + 2] == 0 && a[2][x] == 0 && a[2][x + 1] == 0) {
            if (inc > 0) {
                inc--;
            }
        }
        if (a[1][x - 1] == 1 && a[2][x] == 0 && a[2][x - 2] == 0 && a[2][x - 1] == 0) {
            if (inc > 0) {
                inc--;
            }
        }
    }

    static void tester1(int x, int a[][]) {
        if (a[1][x] == 1 && a[2][x + 1] == 0 && a[2][x - 1] == 0) {
            inc++;
        }
        if (a[1][x + 1] == 1 && a[2][x + 2] == 0 && a[2][x] == 0) {
            inc++;
        }
        if (a[1][x - 1] == 1 && a[2][x] == 0 && a[2][x - 2] == 0) {
            inc++;
        }
    }

    /*
6 5
1 2
1 3
1 4
2 3
1 3

     */
}
//to be fare with you
//the testcase number 7 i just saw the output , and i discover wrong in understanding when the answer equal infinit