#include <bits/stdc++.h>
using namespace std;
const long long int inf = 1000000000;
const long long int mod = 1000000000 + 7;
inline void IO() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
inline int dcmp(long double x) { return x < -1e-12 ? -1 : (x > 1e-12); }
template <class T>
inline int CHECK(T MASK, int i) {
  return (MASK >> i) & 1;
}
template <class T>
inline T ON(T MASK, int i) {
  return MASK | (T(1) << i);
}
template <class T>
inline T OFF(T MASK, int i) {
  return MASK & (~(T(1) << i));
}
template <typename T>
inline int CNT(T MASK) {
  if (numeric_limits<T>::digits <= numeric_limits<unsigned int>::digits)
    return __builtin_popcount(MASK);
  else
    return __builtin_popcountll(MASK);
}
template <class T>
inline int RIGHT(T MASK) {
  return log2(MASK & -MASK);
}
int dx4[] = {0, 0, -1, +1};
int dy4[] = {+1, -1, 0, 0};
int dx8[] = {1, 1, 0, -1, -1, -1, 0, 1, 0};
int dy8[] = {0, 1, 1, 1, 0, -1, -1, -1, 0};
inline void I(int& a) { scanf("%d", &a); }
inline void I(long long int& a) { scanf("%I64d", &a); }
inline void I(unsigned long long int& a) { scanf("%I64u", &a); }
inline void I(char* a) { scanf("%s", a); }
char Iarr[2000010];
inline void I(string& a) {
  scanf("%s", Iarr);
  a = Iarr;
}
template <typename T, typename... Args>
void I(T& a, Args&... args) {
  I(a);
  I(args...);
}
inline void OUT(int a) { printf("%d", a); }
inline void OUT(long long int a) { printf("%I64d", a); }
inline void OUT(const char* a) { printf("%s", a); }
inline void OUT(char* a) { printf("%s", a); }
inline void OUT(bool a) { printf("%d", a); }
inline void OUT(string a) {
  for (__typeof(a.end()) it = (a.begin()) - ((a.begin()) > (a.end()));
       it != (a.end()) - ((a.begin()) > (a.end()));
       it += 1 - 2 * ((a.begin()) > (a.end())))
    printf("%c", *it);
}
inline void OUT(unsigned long long int a) { printf("%I64u", a); }
template <typename T, typename... Args>
void OUT(T a, Args... args) {
  OUT(a);
  OUT(" ");
  OUT(args...);
}
template <typename... Args>
void O(Args... args) {
  OUT(args...);
  OUT("\n");
}
template <typename T1, typename T2>
inline ostream& operator<<(ostream& os, pair<T1, T2> p) {
  os << "{" << p.first << ", " << p.second << "}";
  return os;
}
template <typename T>
inline ostream& operator<<(ostream& os, vector<T>& a) {
  os << "[";
  for (int i = 0; i < (int)a.size(); i++) {
    if (i) os << ", ";
    os << a[i];
  }
  os << "]";
  return os;
}
void err(istream_iterator<string> it) {}
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cout << *it << " = " << a << endl;
  err(++it, args...);
}
const int M = 200010;
int main() {
  int r, s, p;
  I(r, s, p);
  long double dp[r + 1][s + 1][p + 1];
  for (int i = 0; i <= r; i++) {
    for (int j = 0; j <= s; j++) {
      for (int k = 0; k <= p; k++) {
        dp[i][j][k] = 0;
      }
    }
  }
  dp[r][s][p] = 1;
  long double ans[3] = {0};
  for (int i = r; i >= 0; i--) {
    for (int j = s; j >= 0; j--) {
      for (int k = p; k >= 0; k--) {
        long double d =
            (long double)i * j + (long double)i * k + (long double)j * k;
        if (dcmp(d) != 0) {
          if (j) dp[i][j - 1][k] += (((long double)i * j) / d) * dp[i][j][k];
          if (i) dp[i - 1][j][k] += (((long double)i * k) / d) * dp[i][j][k];
          if (k) dp[i][j][k - 1] += (((long double)j * k) / d) * dp[i][j][k];
        }
        if (!i && !j && k) {
          ans[2] += dp[i][j][k];
        }
        if (!i && j && !k) {
          ans[1] += dp[i][j][k];
        }
        if (i && !j && !k) {
          ans[0] += dp[i][j][k];
        }
      }
    }
  }
  cout << setprecision(12) << fixed << ans[0] << " " << ans[1] << " " << ans[2]
       << "\n";
  return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

The Bad Luck Island is inhabited by three kinds of species: r rocks, s scissors and p papers. At some moments of time two random individuals meet (all pairs of individuals can meet equiprobably), and if they belong to different species, then one individual kills the other one: a rock kills scissors, scissors kill paper, and paper kills a rock. Your task is to determine for each species what is the probability that this species will be the only one to inhabit this island after a long enough period of time.

Input

The single line contains three integers r, s and p (1 ≤ r, s, p ≤ 100) — the original number of individuals in the species of rock, scissors and paper, respectively.

Output

Print three space-separated real numbers: the probabilities, at which the rocks, the scissors and the paper will be the only surviving species, respectively. The answer will be considered correct if the relative or absolute error of each number doesn't exceed 10 - 9.

Examples

Input

2 2 2


Output

0.333333333333 0.333333333333 0.333333333333


Input

2 1 2


Output

0.150000000000 0.300000000000 0.550000000000


Input

1 1 3


Output

0.057142857143 0.657142857143 0.285714285714

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const long long int inf = 1000000000;
const long long int mod = 1000000000 + 7;
inline void IO() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
inline int dcmp(long double x) { return x < -1e-12 ? -1 : (x > 1e-12); }
template <class T>
inline int CHECK(T MASK, int i) {
  return (MASK >> i) & 1;
}
template <class T>
inline T ON(T MASK, int i) {
  return MASK | (T(1) << i);
}
template <class T>
inline T OFF(T MASK, int i) {
  return MASK & (~(T(1) << i));
}
template <typename T>
inline int CNT(T MASK) {
  if (numeric_limits<T>::digits <= numeric_limits<unsigned int>::digits)
    return __builtin_popcount(MASK);
  else
    return __builtin_popcountll(MASK);
}
template <class T>
inline int RIGHT(T MASK) {
  return log2(MASK & -MASK);
}
int dx4[] = {0, 0, -1, +1};
int dy4[] = {+1, -1, 0, 0};
int dx8[] = {1, 1, 0, -1, -1, -1, 0, 1, 0};
int dy8[] = {0, 1, 1, 1, 0, -1, -1, -1, 0};
inline void I(int& a) { scanf("%d", &a); }
inline void I(long long int& a) { scanf("%I64d", &a); }
inline void I(unsigned long long int& a) { scanf("%I64u", &a); }
inline void I(char* a) { scanf("%s", a); }
char Iarr[2000010];
inline void I(string& a) {
  scanf("%s", Iarr);
  a = Iarr;
}
template <typename T, typename... Args>
void I(T& a, Args&... args) {
  I(a);
  I(args...);
}
inline void OUT(int a) { printf("%d", a); }
inline void OUT(long long int a) { printf("%I64d", a); }
inline void OUT(const char* a) { printf("%s", a); }
inline void OUT(char* a) { printf("%s", a); }
inline void OUT(bool a) { printf("%d", a); }
inline void OUT(string a) {
  for (__typeof(a.end()) it = (a.begin()) - ((a.begin()) > (a.end()));
       it != (a.end()) - ((a.begin()) > (a.end()));
       it += 1 - 2 * ((a.begin()) > (a.end())))
    printf("%c", *it);
}
inline void OUT(unsigned long long int a) { printf("%I64u", a); }
template <typename T, typename... Args>
void OUT(T a, Args... args) {
  OUT(a);
  OUT(" ");
  OUT(args...);
}
template <typename... Args>
void O(Args... args) {
  OUT(args...);
  OUT("\n");
}
template <typename T1, typename T2>
inline ostream& operator<<(ostream& os, pair<T1, T2> p) {
  os << "{" << p.first << ", " << p.second << "}";
  return os;
}
template <typename T>
inline ostream& operator<<(ostream& os, vector<T>& a) {
  os << "[";
  for (int i = 0; i < (int)a.size(); i++) {
    if (i) os << ", ";
    os << a[i];
  }
  os << "]";
  return os;
}
void err(istream_iterator<string> it) {}
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cout << *it << " = " << a << endl;
  err(++it, args...);
}
const int M = 200010;
int main() {
  int r, s, p;
  I(r, s, p);
  long double dp[r + 1][s + 1][p + 1];
  for (int i = 0; i <= r; i++) {
    for (int j = 0; j <= s; j++) {
      for (int k = 0; k <= p; k++) {
        dp[i][j][k] = 0;
      }
    }
  }
  dp[r][s][p] = 1;
  long double ans[3] = {0};
  for (int i = r; i >= 0; i--) {
    for (int j = s; j >= 0; j--) {
      for (int k = p; k >= 0; k--) {
        long double d =
            (long double)i * j + (long double)i * k + (long double)j * k;
        if (dcmp(d) != 0) {
          if (j) dp[i][j - 1][k] += (((long double)i * j) / d) * dp[i][j][k];
          if (i) dp[i - 1][j][k] += (((long double)i * k) / d) * dp[i][j][k];
          if (k) dp[i][j][k - 1] += (((long double)j * k) / d) * dp[i][j][k];
        }
        if (!i && !j && k) {
          ans[2] += dp[i][j][k];
        }
        if (!i && j && !k) {
          ans[1] += dp[i][j][k];
        }
        if (i && !j && !k) {
          ans[0] += dp[i][j][k];
        }
      }
    }
  }
  cout << setprecision(12) << fixed << ans[0] << " " << ans[1] << " " << ans[2]
       << "\n";
  return 0;
}

```