The Elfstedentocht (English: Eleven Cities Tour) is an almost 200 kilometer long ice skating tour on natural ice. It is held in the province of Friesland in the north of the Netherlands, leading past all eleven historical cities of the province. The first official tour was held in 1909 when 22 men competed. Because a tour can only be organized if ice conditions are suitable, it has only been run 15 times so far. In the past 50 years, the Elfstedentocht has taken place only three times, most recently in 1997. Because of its distance and heroic character, the Elfstedentocht is also called "The Tour of the Tours".

In addition to the eleven historic cities that are always along the route, each edition of the tour may pass through different villages. Leeuwarden — the capital of Friesland — has been the traditional start and finish place. The first four tours (1909–1933) and the seventh tour (1941) were skated counterclockwise. The remaining tours were skated clockwise and visited the eleven cities in this order:

Each participant receives a stamp card upon registration. There are check points in each of the eleven cities where the skaters must show their cards and have them stamped by hand. In addition, there are also three secret check points to prevent participants from traveling part of the route by car. In each of these secret check points, special pliers are used to cut a hole in the card at a fixed location.

All skaters who cross the finish on the Bonkevaart in Leeuwarden before midnight will receive the coveted Elfstedenkruis (English: Eleven Cities Cross) after checking that their stamp card has all the required stamps and holes. Piet Kleine — who had previously won a gold medal at the Olympics for speed skating — was disqualified in 1997 because he missed getting a stamp at Hindeloopen despite video evidence that he had been there.

Assignment

Despite its very conservative nature, the Royal Association of the Eleven Frisian Towns who organizes the Elfstedentocht has decided to somewhat modernize the next edition of the tour. Stamp cards will be automatically checked at the finish line. This way, skaters no longer need to wait so long for their Elfstedenkruis after their journey through hell, as they had to in the past. The organizers ask you to write a computer program to perform this check: a cross may be awarded if and only if the stamp card has exactly eleven stamps and three holes.

Input

A stamp card of the Elfstedentocht containing one or more stamps with city names — each on a separate line — that ends with a line containing finish. Some city names may have one or more holes (��) inserted among their letters.

Output

The report after checking the stamp card. This report consists of three lines containing the following information:

1. number of stamps (cities) on the card

2. number of holes in the card; if there is at least one hole in the card, the number of holes must be followed by a space and a list of all cities with at least one hole in their name, enclosed in parentheses, with holes removed from their name, in the order of the stamps of the card, and separated from each other by a comma and a space

3. decision whether the skater earns a cross (yes) or not (no); a cross may be awarded if and only if the stamp card has exactly eleven stamps and three holes

Check the examples below to see how the report must be formatted.

Example

Input:

Leeuwarden
Sneek
IJlst
Slo��ten
Stavoren
Hindelo��o��pen
Workum
Bolsward
Harlingen
Franeker
Dokkum
finish

Output:

# stamps: 11
# holes: 3 (Sloten, Hindeloopen)
cross earned: yes

Example

Input:

Ljouwert
Snits
Dry��lts
Sleat
Hyl��pen
Boal��sert
Harns
Frjent��sjer
Dokkum
finish

Output:

# stamps: 9
# holes: 4 (Drylts, Hylpen, Boalsert, Frjentsjer)
cross earned: no