Algorithm title: Hdu 3910 Liang Guo Sha

Problem Description

Maybe you know "San Guo sha", but I guess you didn ' t hear the game: "Liang Guo sha"!

Let me introduce this game. Unlike "San Guo Sha" with its complicated rules, "Liang Guo sha" are a simple game, it consists only four cards, two cards Named "Sha", and the other named "Shan".

Alice and Bob are good friends, and they ' re playing "Liang Guo Sha" now. Everyone has two cards:a "Sha" and a "Shan". Each round, everyone choose a. his/her own, and show it Together (Just show the selected. Away). If both of them choose "Sha", then Alice gets a points, and Bob loses a points; If both of them choose "Shan", then Alice gets B points, and Bob loses B points; Otherwise, Bob gets C points, and Alice loses C points.

Both Alice and Bob wants to get points as many as possible, they thought a optimal strategy:calculating a percentage of C Hoosing card "Sha" in order to ensure that even the opponent uses the optimal strategy, he/she can still get a highest NT Exceptation.

Here's the question, if both Alice and Bob use the optimal strategy to do their points, higher is the What Point which Alice can get in a round?

Input

Several test case, process to EOF.

Each test case is has only a line, consists three positive integers:a, B, C respectively.

1 <= A, B, C <= 100000

Output

Each test case just need to output one line, and the expectation point is Alice can get. Round to 6 decimal points.

Sample Input

2 10 4

3 3 3

Sample Output

0.200000

0.000000

Hint

In test Case 1, both Alice and Bob calculated the best percentage of choosing "Sha", and the their percentage the are : 70%.

If Bob does not choose the best percentage, he strategy might be targetd.

For example, if Bob choose 100%, then Alice can change her percentage to 100%, Bob might lose many. Bob is clever, so he won ' t does that.

Reference to the http://blog.csdn.net/ivan_zjj/article/details/7927970

Topic both Alice and Bob wants to get points as many as possible, they thought a optimal strategy:calculating a percentage o F Choosing Card "Sha" in order to ensure that even the opponent uses the optimal strategy, he/she can still get a highest Point Exceptation.

is important

Code:

#include <stdio.h>
int main ()
{
    int a,b,c;
    while (scanf ("%d%d%d", &a,&b,&c)!=eof)
    {
        double x= (double) (b+c)/(a+b+c*2);
        printf ("%.6lf\n", (1-x) *b-x*c);
    }    
    return 0;
}

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