Problem Statement

We have N fuses connected in series. The i-th fuse from the left has a length of A_i centimeters and burns at a constant speed of B_i centimeters per second.
Consider igniting this object from left and right ends simultaneously. Find the distance between the position where the two flames will meet and the left end of the object.

Input

Input is given from Standard Input in the following format:
N
A_1 B_1
A_2 B_2
$\vdots$
A_N B_N

Output

Print the distance between the position where the two flames will meet and the left end of the object, in centimeters (print just the number).
Your output will be considered correct when its absolute or relative error from our answer is at most 10^{-5}.

Constraints

• $1 \leq N \leq 10^5$
• $1 \leq A_i,B_i \leq 1000$
• All values in input are integers.

Sample Input 1

3
1 1
2 1
3 1

Sample Output 1

3.000000000000000

The two flames will meet at 3 centimeters from the left end of the object.

Sample Input 2

3
1 3
2 2
3 1

Sample Output 2

3.833333333333333

Sample Input 3

5
3 9
1 2
4 6
1 5
5 3

Sample Output 3

8.916666666666668

见题面 Input 部分

见题面 Output 部分