Define the following functions:
Given integer N (1 <= n <= 100) and {an} {bn}, for 1 <= i <= N, define:
and
calculate the integral:
Input
A line containing only the integer N is given first.
Then N lines follow, each line has two float-point number Ai and Bi.
There are several test cases, so process to the end of file.
Output
For each testcase, output a line containing only the integer N first.
Then output a second line containing the result of the integral.
The result should be printed in scientific format which has a precision of 10 digits after radix point.
Sample Input
1
0 2
2
1 3
0 4
3
2 4
1 5
0 6
Sample Output
1
0.0000000000e+000
2
8.0000000000e+000
3
7.2000000000e+001
