Function Curve

Given sequences of k₁, k₂, … k_n, a₁, a₂, …, a_n and b₁, b₂, …, b_n. Consider following function:

Then we draw F(x) on a xy-plane, the value of x is in the range of [0,100]. Of course, we can get a curve from that plane.
Can you calculate the length of this curve？

The first line of the input contains one integer T (1<=T<=15), representing the number of test cases.
Then T blocks follow, which describe different test cases.
The first line of a block contains an integer n ( 1 <= n <= 50 ).
Then followed by n lines, each line contains three integers k_i, a_i, b_i ( 0<=a_i, b_i<100, 0<k_i<100 ) .

For each test case, output a real number L which is rounded to 2 digits after the decimal point, means the length of the curve.

2 
3 
1 2 3 
4 5 6 
7 8 9 
1 
4 5 6

215.56 
278.91 

All test cases are generated randomly.

2013 ACM-ICPC吉林通化全国邀请赛——题目重现