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 math
import time
import sys
import os
from math import gcd, floor, sqrt, log
start_time = time.time()
def iin(): return int(input())
def sin(): return input().strip()
def listin(): return list(map(int, input().strip().split()))
def liststr(): return list(map(str, input().strip().split()))
def ceill(x): return int(x) if(x == int(x)) else int(x)+1
def ceilldiv(x, d): x//d if(x % d == 0) else x//d+1
def LCM(a, b): return (a*b)//gcd(a, b)


def solve():
    a, b, c = listin()
    if a == 0:
        if b == 0:
            if c == 0:
                print(-1)
                return
            print(0)
            return
        print(1)

        print("{0:.10f}".format((-1*c)/b))
        return
    d = b**2 - (4*a*c)
    if d < 0:
        print(0)
        return
    x = set()
    x.add(((-1*b)-sqrt(d))/(2*a))
    x.add(((-1*b)+sqrt(d))/(2*a))
    x = list(x)
    x.sort()
    print(len(x))
    for i in x:
        print("{0:.10f}".format(i))


t = 1
# t = int(input())
for hula in range(t):
    solve()
sys.stderr.write(str(time.time()-start_time))