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;
inline long long int max(long long int a, long long int b, long long int c) {
  return max(max(a, b), c);
}
inline long long int min(long long int a, long long int b, long long int c) {
  return min(min(a, b), c);
}
inline long long int max(long long int a, long long int b) {
  return (a > b) ? a : b;
}
inline long long int min(long long int a, long long int b) {
  return (a < b) ? a : b;
}
inline long long int add(long long int x, long long int y, long long int mod_) {
  return (x + y >= mod_) ? x + y - mod_ : x + y;
}
inline long long int mul(long long int x, long long int y, long long int mod_) {
  return ((x % mod_) * 1LL * (y % mod_)) % mod_;
}
long long int power(long long int a, long long int n) {
  long long int p = 1;
  while (n > 0) {
    if (n % 2) {
      p = p * a;
    }
    n >>= 1;
    a *= a;
  }
  return p;
}
long long int powm(long long int a, long long int n, long long int mod_) {
  long long int p = 1;
  while (n) {
    if (n % 2) {
      p = mul(p, a, mod_);
    }
    n >>= 1;
    a = mul(a, a, mod_);
  }
  return p % mod_;
}
long long int powi(long long int a, long long int mod_) {
  return powm(a, mod_ - 2, mod_);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  ;
  cout << setprecision(15);
  long long int mn, mx;
  long long int n, m, t, k, i, j, sum = 0, flag = 0, cnt = 0;
  long long int x = 0, y = 0, z, l, r, q;
  int TC = 1;
  while (TC--) {
    double a, b, c;
    cin >> a >> b >> c;
    if (a != 0) {
      if (b * b - 4 * a * c < 0)
        cout << 0;
      else if (b * b - 4 * a * c == 0)
        cout << 1 << '\n' << (-b) / (2.0 * a);
      else {
        cout << "2\n";
        double D = sqrtl(b * b - 4 * a * c);
        double x = (-b + D) / (2.0 * a);
        double y = (-b - D) / (2.0 * a);
        if (x < y) {
          cout << x << '\n' << y;
        } else
          cout << y << '\n' << x;
      }
    } else if (b != 0) {
      cout << 1 << '\n' << (-c / b);
    } else {
      if (c != 0)
        cout << 0;
      else
        cout << -1;
    }
  }
  cerr << "Time : " << 1000 * ((double)clock()) / (double)CLOCKS_PER_SEC
       << "ms\n";
  return 0;
}