Contest Duration: - (local time) (100 minutes) Back to Home
D - increment of coins /

Time Limit: 2 sec / Memory Limit: 1024 MB

制約

• 0 \leq A,B,C \leq 99
• A+B+C \geq 1

入力

A B C


入力例 1

99 99 99


出力例 1

1.000000000


1 回目の操作でどの硬貨を取り出しても、取り出した種類の硬貨が 100 枚になります。

入力例 2

98 99 99


出力例 2

1.331081081


1 回目の操作で金貨を取り出したときのみ 2 回の操作を行います。 よって期待値は 2\times \frac{98}{98+99+99}+1\times \frac{99}{98+99+99}+1\times \frac{99}{98+99+99}=1.331081081\ldots となります。

入力例 3

0 0 1


出力例 3

99.000000000


入力例 4

31 41 59


出力例 4

91.835008202


Score : 400 points

Problem Statement

We have a bag containing A gold coins, B silver coins, and C bronze coins.

Until the bag contains 100 coins of the same color, we will repeat the following operation:

Operation: Randomly take out one coin from the bag. (Every coin has an equal probability of being chosen.) Then, put back into the bag two coins of the same kind as the removed coin.

Find the expected value of the number of times the operation is done.

Constraints

• 0 \leq A,B,C \leq 99
• A+B+C \geq 1

Input

Input is given from Standard Input in the following format:

A B C


Output

Print the expected value of the number of times the operation is done. Your output will be accepted if its absolute or relative error from the correct value is at most 10^{-6}.

Sample Input 1

99 99 99


Sample Output 1

1.000000000


No matter what coin we take out in the first operation, the bag will contain 100 coins of that kind.

Sample Input 2

98 99 99


Sample Output 2

1.331081081


We will do the second operation only if we take out a gold coin in the first operation. Thus, the expected number of operations is 2\times \frac{98}{98+99+99}+1\times \frac{99}{98+99+99}+1\times \frac{99}{98+99+99}=1.331081081\ldots

Sample Input 3

0 0 1


Sample Output 3

99.000000000


Each operation adds a bronze coin.

Sample Input 4

31 41 59


Sample Output 4

91.835008202