Circle and segment

Find out how many points of intersection of the circle are given by the center coordinates (X, Y) and radius R, and the segment specified by the coordinates of its ends (X_1, Y_1), (X_2, Y_2).

Input

Seven integers X, Y, R, X_1, Y_1, X_2, Y_2, whose moduli do not exceed 1000.

Output

The number of intersection points.

Examples