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 PYTHON3):

Solution:
import os
import sys
from io import BytesIO, IOBase
import math
from queue import Queue
import collections
import itertools
import bisect
import heapq
#sys.setrecursionlimit(100000)
#^^^TAKE CARE FOR MEMORY LIMIT^^^
import random
def main():
    pass
BUFSIZE = 8192
class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")


def binary(n):
    return (bin(n).replace("0b", ""))


def decimal(s):
    return (int(s, 2))


def pow2(n):
    p = 0
    while (n > 1):
        n //= 2
        p += 1
    return (p)


def primeFactors(n):
    l = []
    while n % 2 == 0:
        l.append(2)
        n = n / 2
    for i in range(3, int(math.sqrt(n)) + 1, 2):
        while n % i == 0:
            l.append(i)
            n = n / i
    if n > 2:
        l.append(int(n))
    return (l)


def isPrime(n):
    if (n == 1):
        return (False)
    else:
        root = int(n ** 0.5)
        root += 1
        for i in range(2, root):
            if (n % i == 0):
                return (False)
        return (True)


def maxPrimeFactors(n):
    maxPrime = -1
    while n % 2 == 0:
        maxPrime = 2
        n >>= 1
    for i in range(3, int(math.sqrt(n)) + 1, 2):
        while n % i == 0:
            maxPrime = i
            n = n / i
    if n > 2:
        maxPrime = n
    return int(maxPrime)


def countcon(s, i):
    c = 0
    ch = s[i]
    for i in range(i, len(s)):
        if (s[i] == ch):
            c += 1
        else:
            break
    return (c)


def lis(arr):
    n = len(arr)
    lis = [1] * n
    for i in range(1, n):
        for j in range(0, i):
            if arr[i] > arr[j] and lis[i] < lis[j] + 1:
                lis[i] = lis[j] + 1
    maximum = 0
    for i in range(n):
        maximum = max(maximum, lis[i])
    return maximum
def isSubSequence(str1, str2):
    m = len(str1)
    n = len(str2)
    j = 0
    i = 0
    while j < m and i < n:
        if str1[j] == str2[i]:
            j = j + 1
        i = i + 1
    return j == m
def maxfac(n):
    root = int(n ** 0.5)
    for i in range(2, root + 1):
        if (n % i == 0):
            return (n // i)
    return (n)
def p2(n):
    c=0
    while(n%2==0):
        n//=2
        c+=1
    return c
def seive(n):
    primes=[True]*(n+1)
    primes[1]=primes[0]=False
    i=2
    while(i*i<=n):
        if(primes[i]==True):
            for j in range(i*i,n+1,i):
                primes[j]=False
        i+=1
    pr=[]
    for i in range(0,n+1):
        if(primes[i]):
            pr.append(i)
    return pr
def ncr(n, r, p):
    num = den = 1
    for i in range(r):
        num = (num * (n - i)) % p
        den = (den * (i + 1)) % p
    return (num * pow(den,
            p - 2, p)) % p
def denofactinverse(n,m):
    fac=1
    for i in range(1,n+1):
        fac=(fac*i)%m
    return (pow(fac,m-2,m))
def numofact(n,m):
    fac=1
    for i in range(1,n+1):
        fac=(fac*i)%m
    return(fac)
def sod(n):
    s=0
    while(n>0):
        s+=n%10
        n//=10
    return s
a,b,c=map(int,input().split())
d=b*b-4*a*c
if(a==0):
    if(b==0 and c==0):
        print(-1)
    elif(b==0 and c!=0):
        print(0)
    else:
        print(1)
        print(-c/b)
else:
    if(d<0):
        print(0)
    elif(d==0):
        #print("HEY")
        print(1)
        print(-b/(2*a))
    else:
        #print(d,b,a,d**0.5)
        t=d**0.5
        #print(t)
        r1=(-b+t)/(2*a)
        r2=(-b-t)/(2*a)
        r1,r2=min(r1,r2),max(r1,r2)
        print(2)
        print(r1)
        print(r2)