Neko is running away! Eve wants to catch him. At first, Eve is standing at the point with coordinates \((x_1,y_1)\), while Neko is standing at the point with coordinates \((x_2,y_2)\). For every minute, Eve can choose to go up, down, left, or right with 1 unit distance. For instance, if she is at \((x,y)\) now, she can go to \((x,y+1),(x,y-1),(x-1,y)\) or \((x+1,y)\).
Eve noticed that Neko also moves 1 unit distance every minute, but he only moves according to a sequence periodically. The sequence only contains 'U','D','L','R', denoting that Neko moves up, down, left, right respectively.
Eve is now wondering how many minutes she needs at least to catch Neko.