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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int TestMillerRabin[12] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37};
long long mulmod(long long a, long long b, long long p) {
  long long x = 0, y = a % p;
  while (b > 0) {
    if (b % 2 == 1) x = (x + y) % p;
    y = (1LL * y * 2) % p;
    b = b / 2;
  }
  return x % p;
}
long long fastexp(long long x, long long y, long long p) {
  long long ans = 1;
  while (y > 0) {
    if (y & 1) ans = (1LL * ans * x) % p;
    y = y >> 1;
    x = (1LL * x * x) % p;
  }
  return ans % p;
}
long long fastexpp(long long x, long long y, long long p) {
  long long ans = 1;
  while (y > 0) {
    if (y & 1) ans = mulmod(ans, x, p);
    y = y >> 1;
    x = mulmod(x, x, p);
  }
  return ans % p;
}
long long invmod(long long x, long long p) { return fastexp(x, p - 2, p) % p; }
bool check_composite(long long n, long long a, long long d, int s) {
  long long x = fastexp(a, d, n);
  if (x == 1 || x == n - 1) return false;
  for (int r = 1; r < s; r++) {
    x = (1LL * x * x) % n;
    if (x == n - 1) return false;
  }
  return true;
}
bool isPrime(long long p) {
  if (p <= 1) return false;
  int r = 0;
  long long d = p - 1;
  while (!(d & 1)) {
    d >>= 1;
    r++;
  }
  for (int i = 0; i < 12; i++) {
    int value = TestMillerRabin[i];
    if (p == value) return true;
    if (check_composite(p, value, d, r)) return false;
  }
  return true;
}
int main() {
  int A, B, C;
  cin >> A >> B >> C;
  if (A == 0) {
    if (B == 0) {
      if (C == 0)
        cout << "-1\n";
      else
        cout << "0\n";
    } else {
      cout << 1 << '\n';
      double ans = -1 * (double)C / (double)B;
      printf("%.5lf\n", ans);
    }
  } else {
    long long det = 1LL * B * B - 4LL * A * C;
    if (det > 0) {
      cout << "2\n";
      double ans1 = (-B + sqrt((double)det)) / (2 * (double)A);
      double ans2 = (-B - sqrt((double)det)) / (2 * (double)A);
      if (ans1 > ans2) {
        double aux = ans1;
        ans1 = ans2;
        ans2 = aux;
      }
      printf("%.8lf\n%.8lf\n", ans1, ans2);
      return 0;
    }
    if (det == 0) {
      cout << "1\n";
      double ans = -1 * (double)B / (2 * (double)A);
      printf("%.8lf\n", ans);
    } else {
      cout << "0\n";
    }
  }
  return 0;
}