Rock Skipping

As a member of the International Rock-Skipping League, you travel to a different lake each week and compete in a rock-skipping contest. The goal is to throw a rock so that it skips on the water as many times as possible; the exact rules for determining the winner are given below. To make the competitions interesting, the League often chooses lakes with logs, sandbars, and other obstacles.

A lake is given as a side-view, water-level "map", like the first line of the example below (the numbers 0..29 beneath the map are just for reference). A period . indicates clear water, where a rock will skip; any other character indicates an obstacle that will stop a rock.

...=...**..#...@....:.:.:..=..
______________________________
          11111111112222222222
012345678901234567890123456789

You stand at the left end of the lake. You can throw a rock so that it first lands at any position in the lake and then skips at a fixed interval thereafter. So a throw is a pair (i, d), where i (i ≥ 0) is the initial landing position and d (d > 0) is the distance between skips. Note that d must be positive.

The count of a throw is the number of times it skips on the water. The length of a throw is the position of its last contact with either water or an obstacle. To rank two distinct throws, apply the following criteria in order until a winner is determined:

1. count: the higher value wins.
2. length: the greater value wins.
3. initial position i: the greater value wins.
4. distance between skips d: the smaller value wins.

For the map above, throw (27, 2) hits the obstacle at position 27; it has count 0 and length 27. Throw (16, 1) skips at positions 16, 17, 18, and 19, then hits the obstacle at position 20; it has count 4 and length 20, so it beats (27, 2). Throw (2, 7) skips at positions 2, 9, 16, and 23, then skips over the lake; it has count 4 and length 23, so it beats (16, 1). Throw (1, 4) skips at positions 1, 5, 9, 13, 17, 21, 25, and 29, then skips over the lake; it has count 8 and length 29, and is the best possible throw for this lake.

The input consists of one or more lake maps, each on a line by itself and 1 to 40 characters long, followed by a line containing only END that marks the end of the input. Positions within a map are numbered starting from zero. A map contains only printable ASCII punctuation characters. A period . indicates clear water and any other character indicates an obstacle.

For each map, compute the best possible throw (i, d) and print a line containing i and d separated by a single space.