22150_Poo

There is a pool which is circular shape, the centre of the pool is located at (0, 0). And there is a bridge cross over the pool, the bridge is considered as a straight line segment AB on the plane, points A and B are both on the boundary of the pool.

Merlin wants to go from points F to G, F and G are also on the boundary of the pool, but he cannot swim. Write a program to tell him the shortest distance from F to G.

Input contains multiple test cases.

The first line of each test case contains an integers R ( 1 ≤ R ≤ 100 ), representing the radius of the pool.

The second line contains eight real numbers X_A, Y_A, X_B, Y_B, X_F, Y_F, X_G, Y_G, representing the coordinates of points A, B, F and G. Each coordinate satisfies |X²+Y²-R²| < 10^-8.

Output the answer on a single line for each test case, round to two digits after decimal point.

1
0.729627 -0.683845334 0.198022 -0.9801975758 0.314911 -0.9491212052 -0.735596 -0.6774204933
1
0.517308 0.8557992949 0.936038 -0.351898938 0.396901 -0.9178614254 0.616543 -0.7873212363

1.15
0.26