#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline void read(T& x) {
  x = 0;
  char c;
  while (!isdigit(c = getchar()))
    ;
  do {
    x = x * 10 + c - '0';
  } while (isdigit(c = getchar()));
}
template <typename T>
inline void write(T x) {
  if (x > 9) write(x / 10);
  putchar(x % 10 + 48);
}
void Write(string s) {
  for (int i = 0; i < s.length(); i++) {
    putchar(s[i]);
  }
}
void Sangnt(bool nt[], int n) {
  int x = sqrt(n);
  nt[0] = true, nt[1] = true;
  for (int i = 2; i <= x; i++) {
    if (nt[i] == false) {
      for (int j = i * i; j <= n; j += i) {
        nt[j] = true;
      }
    }
  }
}
void Congdon(int a[], int n) {
  for (int i = 1; i < n; i++) {
    a[i] += a[i - 1];
  }
}
unsigned long long POW(int a, int b) {
  if (b == 0) return 1;
  unsigned long long y = POW(a, b / 2);
  if (b % 2 == 0)
    return y * y;
  else
    return y * y * a;
}
long long UCLN(long long x, long long y) {
  long long r, a, b;
  a = max(x, y), b = min(x, y);
  while (b) {
    r = a % b;
    a = b, b = r;
  }
  return a;
}
string add(string a, string b) {
  string ans;
  while (a.length() < b.length()) a = '0' + a;
  while (b.length() < a.length()) b = '0' + b;
  ans = a;
  int n = ans.length();
  int digit, Add = 0;
  for (int i = n - 1; i >= 0; i--) {
    digit = (a[i] - '0' + b[i] - '0' + Add) % 10;
    Add = (a[i] - '0' + b[i] - '0' + Add) / 10;
    ans[i] = digit + '0';
  }
  if (Add == 1) ans = '1' + ans;
  while (ans[0] == '0' and ans.length() > 1) ans.erase(0, 1);
  return ans;
}
string Minu(string a, string b) {
  string ans;
  while (a.length() < b.length()) a = '0' + a;
  while (b.length() < a.length()) b = '0' + b;
  ans = a;
  int n = ans.length();
  int digit, Add = 0;
  for (int i = n - 1; i >= 0; i--) {
    digit = a[i] - b[i] - Add;
    if (digit < 0) {
      digit = digit + 10;
      Add = 1;
    } else
      Add = 0;
    ans[i] = digit + '0';
  }
  while (ans[0] == '0' and ans.length() > 1) ans.erase(0, 1);
  return ans;
}
double a, b, c, x, y;
int main() {
  ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL);
  cin >> a >> b >> c;
  if (a == 0) {
    if (b == 0) {
      if (c == 0) {
        cout << -1;
      } else {
        cout << 0;
      }
    } else {
      cout << 1 << endl;
      printf("%.10f", -c / b);
    }
  } else {
    double delta = b * b - 4 * a * c;
    if (delta == 0) {
      x = -b / 2 / a;
      cout << 1 << endl;
      printf("%.10f", x);
    } else if (delta < 0) {
      cout << 0;
    } else {
      cout << 2 << endl;
      x = -(b + sqrt(delta)) / 2 / a;
      y = -(b - sqrt(delta)) / 2 / a;
      if (x > y) {
        swap(x, y);
      }
      printf("%.10f\n", x);
      printf("%.10f", y);
    }
  }
  return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline void read(T& x) {
  x = 0;
  char c;
  while (!isdigit(c = getchar()))
    ;
  do {
    x = x * 10 + c - '0';
  } while (isdigit(c = getchar()));
}
template <typename T>
inline void write(T x) {
  if (x > 9) write(x / 10);
  putchar(x % 10 + 48);
}
void Write(string s) {
  for (int i = 0; i < s.length(); i++) {
    putchar(s[i]);
  }
}
void Sangnt(bool nt[], int n) {
  int x = sqrt(n);
  nt[0] = true, nt[1] = true;
  for (int i = 2; i <= x; i++) {
    if (nt[i] == false) {
      for (int j = i * i; j <= n; j += i) {
        nt[j] = true;
      }
    }
  }
}
void Congdon(int a[], int n) {
  for (int i = 1; i < n; i++) {
    a[i] += a[i - 1];
  }
}
unsigned long long POW(int a, int b) {
  if (b == 0) return 1;
  unsigned long long y = POW(a, b / 2);
  if (b % 2 == 0)
    return y * y;
  else
    return y * y * a;
}
long long UCLN(long long x, long long y) {
  long long r, a, b;
  a = max(x, y), b = min(x, y);
  while (b) {
    r = a % b;
    a = b, b = r;
  }
  return a;
}
string add(string a, string b) {
  string ans;
  while (a.length() < b.length()) a = '0' + a;
  while (b.length() < a.length()) b = '0' + b;
  ans = a;
  int n = ans.length();
  int digit, Add = 0;
  for (int i = n - 1; i >= 0; i--) {
    digit = (a[i] - '0' + b[i] - '0' + Add) % 10;
    Add = (a[i] - '0' + b[i] - '0' + Add) / 10;
    ans[i] = digit + '0';
  }
  if (Add == 1) ans = '1' + ans;
  while (ans[0] == '0' and ans.length() > 1) ans.erase(0, 1);
  return ans;
}
string Minu(string a, string b) {
  string ans;
  while (a.length() < b.length()) a = '0' + a;
  while (b.length() < a.length()) b = '0' + b;
  ans = a;
  int n = ans.length();
  int digit, Add = 0;
  for (int i = n - 1; i >= 0; i--) {
    digit = a[i] - b[i] - Add;
    if (digit < 0) {
      digit = digit + 10;
      Add = 1;
    } else
      Add = 0;
    ans[i] = digit + '0';
  }
  while (ans[0] == '0' and ans.length() > 1) ans.erase(0, 1);
  return ans;
}
double a, b, c, x, y;
int main() {
  ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL);
  cin >> a >> b >> c;
  if (a == 0) {
    if (b == 0) {
      if (c == 0) {
        cout << -1;
      } else {
        cout << 0;
      }
    } else {
      cout << 1 << endl;
      printf("%.10f", -c / b);
    }
  } else {
    double delta = b * b - 4 * a * c;
    if (delta == 0) {
      x = -b / 2 / a;
      cout << 1 << endl;
      printf("%.10f", x);
    } else if (delta < 0) {
      cout << 0;
    } else {
      cout << 2 << endl;
      x = -(b + sqrt(delta)) / 2 / a;
      y = -(b - sqrt(delta)) / 2 / a;
      if (x > y) {
        swap(x, y);
      }
      printf("%.10f\n", x);
      printf("%.10f", y);
    }
  }
  return 0;
}

```