Problem C
Tunnelling the Earth
For example, travelling from Waterloo to Cairo requires a distance of $9\, 293\, 521$ metres following the great circle route around the earth, but only $8\, 491\, 188$ metres following the straight line through the earth.
For this problem, assume that the earth is a perfect sphere with radius of exactly $6\, 371\, 009$ metres.
Input
The first line of input contains a single integer $1 \le T \le 1000$, the number of test cases to follow. Each test case is one line containing four floating point numbers $\text {lat}_1$, $\text {long}_1$, $\text {lat}_2$ and $\text {long}_2$ ($-90 \le \text {lat}_1, \text {lat}_2 \le 90$, $-180 \le \text {long}_1, \text {long}_2 \le 180$), where $\text {lat}_1$, $\text {long}_1$ are the latitude and longitude of the origin of the trip, and $\text {lat}_2, \text {long}_2$ are the latitude and longitude of the destination of the trip. All of these measurements are in degrees. Positive numbers indicate North latitude and East longitude, while negative numbers indicate South latitude and West longitude.
Output
For each test case, output a line containing a single real number, the difference in the distance between the two points following the great circle route around the surface of the earth and following the straight line through the earth, in metres. Your answer should have an absolute or relative error of at most $10^{-7}$.
| Sample Input 1 | Sample Output 1 |
|---|---|
1 43.466667 -80.516667 30.058056 31.228889 |
802332.5872422839 |
