Calculate the Integral

Time Limit: 1 Second    Memory Limit: 32768 KB

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

Submit

Source: ZOJ Monthly, May 2003