Map websites such as Bing Maps and Google Maps often store their maps as many different image files, called tiles. The lowest zoom level (level 0) consists of a single tile with a low-detail image of the whole map, zoom level1consists of four tiles each containing a slightly more detailed version of a quarter of the map, and in general zoom levelncontains4ndifferent tiles that each contain a part of the map.
One way of identifying a tile is by means of a quadkey. A quadkey is a string of digits uniquely identifying a tile at a certain zoom level. The first digit specifies in which of the four quadrants of the whole map the tile lies: 0 for the top-left quadrant, 1 for the top-right quadrant, 2 for the bottom-left quadrant and 3 for the bottom-right quadrant. The subsequent digits specify in which sub quadrant of the current quadrant the tile is. The quad keys for zoom levels 1 to 3 are shown in Figure I.1(a).
Another way of identifying a tile is to give the zoom level and x and y coordinates, where (0, 0) is the left-top corner. The coordinates for the tiles of zoom level 3 are shown in Figure I.1(b). Given the quadkey of a tile, output the zoom level and x and y coordinates of that tile.
The input consists of:
Output three integers, the zoom level and the x and y coordinates of the tile.
1 1 1
3 6 2