Function Curve
TimeLimit:1000MS MemoryLimit:65535KB
64-bit integer IO format:%I64d
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Problem Description
Given sequences of k
1, k
2, … k
n, a
1, a
2, …, a
n and b
1, b
2, …, 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？
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？
Input
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 ) .
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 ) .
Output
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.
SampleInput
2 3 1 2 3 4 5 6 7 8 9 1 4 5 6
SampleOutput
215.56 278.91 Hint All test cases are generated randomly.