```Description

Farmer John has arranged his N (1 ¡Ü N ¡Ü 5,000) cows in a row and many of them are facing forward,
like good cows, Some of them are facing backward, though, and he needs them all to face forward to
make his life perfect.

Fortunately, FJ recently bought an automatic cow turning machine. Since he purchased the discount
model, it must be irrevocably preset to turn K (1 ¡Ü K ¡Ü N) cows at once, and it can only turn cows
that are all standing next to each other in line. Each time the machine is used, it reverses the
facing direction of a contiguous group of K cows in the line (one cannot use it on fewer than K
cows, e.g., at the either end of the line of cows). Each cow remains in the same *location* as
before, but ends up facing the *opposite direction*. A cow that starts out facing forward will
be turned backward by the machine and vice-versa.

value of K that minimizes the number of operations required by the machine to make all the cows
face forward. Also determine M, the minimum number of machine operations required to get all the
cows facing forward using that value of K.

Input

The input contains multiple test cases.
For each test case:
* Line 1: A single integer: N
* Lines 2..N + 1: Line i+1 contains a single character, F or B, indicating whether cow i is
facing forward or backward.

Output

* Line 1: Two space-separated integers: K and M

Sample Input

7
B
B
F
B
F
B
B

Sample Output

3 3

Hint

There are seven cows and they are facing
backward, backward, forward, backward, forward, backward, and backward, respectively.

For K = 3, the machine must be operated three times: turn cows (1,2,3), (3,4,5), and finally (5,6,7):

B > F   F   F
B > F   F   F
F > B > F   F
B   B > F   F
F   F > B > F
B   B   B > F
B   B   B > F

Source

USACO March 07 Gold
```