Given sequences of k1, k2, … kn, a1, a2, …, an and b1, b2, …, bn. 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?
输入解释
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 ki, ai, bi ( 0<=ai, bi<100, 0<ki<100 ) .
输出解释
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.