Four circus flies stand on the four corners of a one inch square shown blue in the pic. When the ringmaster blows his whistle each fly begins to walk directly towards the next fly in a clockwise direction, as shown by the green arrows. As each fly walks is turns so it continues to walk directly towards the next fly, so its direction of motion is always at right angles to the direction of motion of the next fly. Thus each fly walks a curved path and they meet in the middle as shown in red. How far does each fly walk?