Max has just started grade ~9~, and he is in his math class, learning equations of lines!

Max defines the slope-intercept form of a line as the equation of the line in the form ~y = mx + b~. Max is given ~N~ lines in slope-intercept form, each with a distinct ~m~ and ~b~. Max wants to see, at some integer ~x~, the maximum possible ~y~ value out of all the ~N~ lines. He wants to test all integer values of ~x~ in the range ~[1,10^5]~, and wants the sum of these ~y~ values.

Not knowing how to do it, he has asked you to do it for him! Help him!

Input Specification

The first line will contain the integer ~N~ ~(1 \le N \le 10^5)~, the number of lines.

The next ~N~ lines will each contain two integers, ~m, b~ ~(-10^6 \le m, b \le 10^6)~. It is guaranteed both ~m~ and ~b~ are distinct.

Output Specification

On the first line, output the sum of the maximum possible ~y~ values for every integer ~x~ in the range ~[1, 10^5]~. Note that 64-bit integers may be required to pass.

Subtasks

Subtask 1 [40%]

~N \le 10~

Subtask 2 [60%]

No further constraints.

Sample Input 1

3
4 2
-4 -6
0 -2

Sample Output 1

20000400000

Sample Input 2

2
-1 1000
1 -1000

Sample Output 2

4901049000