The distance between the segments

Given two segments in space (x_1; y_1; z_1) - (x_2; y_2; z_2) and (x_3; y_3; z_3) - (x_4; y_4; z_4). Find the distance between the segments.

Input

Given integers x_1; y_1; z_1; x_2; y_2; z_2; x_3; y_3; z_3; x_4; y_4; z_4. The coordinates do not exceed 1000.

Output

Print the distance between the segments with at least 6 digits after the decimal point.

Examples