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

Difficulty: interview

Starter code:

Solutions:
r, s, p = list(map(int, input().split()))
dp = [[[0] * (p+1) for _ in range(s+1)] for _ in range(r+1)]
dp[r][s][p] = 1
def nCk(n, k):
    if n <= k:
        return 1
    res = 1
    for i in range(k):
        res *= n-i
    for i in range(k):
        res //= (i+1)
    return res

C = [nCk(i, 2) for i in range(r+s+p+1)]
for ri in range(r, -1, -1):
    for si in range(s, -1, -1):
        for pi in range(p, -1, -1):
            t = ri * si + si * pi + pi * ri
            if t == 0: continue
            if ri > 0:
                dp[ri-1][si][pi] += dp[ri][si][pi] * ri * pi / t
            if si > 0:
                dp[ri][si-1][pi] += dp[ri][si][pi] * ri * si / t
            if pi > 0:
                dp[ri][si][pi-1] += dp[ri][si][pi] * si * pi / t
        
        
r_sum = sum([dp[ri][0][0] for ri in range(r+1)])
s_sum = sum([dp[0][si][0] for si in range(s+1)])
p_sum = sum([dp[0][0][pi] for pi in range(p+1)])
print(r_sum, s_sum, p_sum)


r, s, p = map(int, input().split())
n = 101
g = lambda i, j, k: i + n * (j + n * k)
t = [0] * (n ** 3)
for i in range(1, n):
    for j in range(n):
        for k in range(n):
            l = g(i, j, k)
            if j or k:
                x, y, z = g(i, j - 1, k), g(i - 1, j, k), g(i, j, k - 1)
                a, b, c = i * j, i * k, j * k
                t[l] = (a * t[x] + b * t[y] + c * t[z]) / (a + b + c)
            else: t[l] = 1
x, y, z = g(r, s, p), g(s, p, r), g(p, r, s)
print(t[x], t[y], t[z])

r, s, p = map(int, input().split())
n = 101
m = n * n
t = [0] * n * m
for i in range(1, n):
    for j in range(n):
        for k in range(n):
            d = i + n * j + m * k
            a = i * j * t[d - n] + i * k * t[d - 1] + j * k * t[d - m]
            b = i * j + i * k + j * k
            t[d] = a / b if j or k else 1
print(t[r + n * s + m * p], t[s + n * p + m * r], t[p + n * r + m * s])

r, s, p = [int(x) for x in input().split()]
dp = [[[0 for i in range(105)] for j in range(105)] for k in range(105)]

dp[r][s][p] = 1

for i in range(r, -1, -1):
    for j in range(s, -1, -1):
        for k in range(p,-1, -1):

            dnr = i * j + j * k + i * k

            if i > 0 and j > 0:
                dp[i][j - 1][k] += (i * j * dp[i][j][k]) / dnr
            if j > 0 and k > 0:
                dp[i][j][k - 1] += (j * k * dp[i][j][k]) / dnr
            if k > 0 and i > 0:
                dp[i - 1][j][k] += (k * i * dp[i][j][k]) / dnr

roc, sci, pap = [0] * 3

for i in range(105):
    roc += dp[i][0][0]
    sci += dp[0][i][0]
    pap += dp[0][0][i]


print(roc, sci, pap)
            

            


r, s, p = [int(x) for x in input().split()]
dp = [[[0 for i in range(105)] for j in range(105)] for k in range(105)]
 
dp[r][s][p] = 1
 
for i in range(r, -1, -1):
    for j in range(s, -1, -1):
        for k in range(p,-1, -1):
 
            dnr = i * j + j * k + i * k
 
            if i > 0 and j > 0:
                dp[i][j - 1][k] += (i * j * dp[i][j][k]) / dnr
            if j > 0 and k > 0:
                dp[i][j][k - 1] += (j * k * dp[i][j][k]) / dnr
            if k > 0 and i > 0:
                dp[i - 1][j][k] += (k * i * dp[i][j][k]) / dnr
 
roc, sci, pap = [0] * 3
 
for i in range(105):
    roc += dp[i][0][0]
    sci += dp[0][i][0]
    pap += dp[0][0][i]
 
 
print(roc, sci, pap)

A, B, C = map(lambda x: int(x)+1, input().split())
M = max(max(A, B), C)
p = [[[0] * (M) for i in range(M)] for j in range(M)]

for a in range(M):
    for b in range(M):
        for c in range(M):
            val=0    
            if a == 0 or b == 0:
                val=0
            elif c == 0:
                val=1
            else:
                div = a*b + b*c + c*a
                val = (a*b) / div * p[a][b-1][c] + \
                      (b*c) / div * p[a][b][c-1] + \
                      (a*c) / div * p[a-1][b][c]
            
            p[a][b][c]=val    
            
print(p[A-1][B-1][C-1], p[B-1][C-1][A-1], p[C-1][A-1][B-1])