Problem: 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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long double eps = 1e-7;
const string alpha = "abcdefghijklmnopqrstuvwxyz";
int d8x[8] = {+1, +1, +1, 0, 0, -1, -1, -1};
int d8y[8] = {+1, 0, -1, +1, -1, +1, 0, -1};
int d4x[4] = {1, 0, 0, -1};
int d4y[4] = {0, -1, 1, 0};
long long power(long long x, long long y) {
  long long fk = 1;
  x = x;
  while (y > 0) {
    if (y & 1) fk = (fk * x);
    y = y >> 1;
    x = (x * x);
  }
  return fk;
}
long long sqr(long long x) { return x * x; }
template <typename T>
T gcd(T a, T b) {
  if (a == 0) return b;
  return gcd(b % a, a);
}
template <class T>
inline void chmax(T &x, T y) {
  x = max((x), (y));
}
template <class T>
inline void chmin(T &x, T y) {
  x = min((x), (y));
}
template <class T>
T abs(T x) {
  return x > 0 ? x : -x;
}
template <typename T>
T powm(T a, T b, long long m) {
  T cnt = 1;
  while (b > 0) {
    if (b % 2 == 1) cnt = (cnt * a) % m;
    b /= 2;
    a = (a * a) % m;
  }
  return cnt % m;
}
long long ncr(long long n, long long r) {
  long long fk = 1;
  if (r > n) return 0;
  if (r > n - r) r = n - r;
  for (long long i = 0; i < r; i++) {
    fk *= (n - i);
    fk /= (i + 1);
  }
  return fk;
}
const int MOD = 998244353;
const int N = 102;
int r, p, s;
long double cache[N][N][N];
bool vis[N][N][N];
long double dp(int a, int b, int c) {
  if (a < 0 or b < 0 or c < 0) return 0;
  if (a == 0) return 0;
  if (a > 0 and b + c == 0) return 1.0;
  long double &ans = cache[a][b][c];
  if (vis[a][b][c]) return cache[a][b][c];
  ans = 0;
  vis[a][b][c] = 1;
  long double tot = a * b + b * c + a * c;
  ans = (a * b * dp(a, b - 1, c) + a * c * dp(a - 1, b, c) +
         b * c * dp(a, b, c - 1)) /
        tot;
  return ans;
}
void solve() {
  cin >> r >> s >> p;
  cout << fixed << setprecision(20);
  cout << dp(r, s, p) << ' ' << dp(s, p, r) << ' ' << dp(p, r, s);
}
int32_t main() {
  cin.sync_with_stdio(0);
  cin.tie(0);
  cin.exceptions(cin.failbit);
  int tc = 1;
  for (int i = 1; i <= tc; ++i) {
    solve();
  }
  return 0;
}