FOOTBALL - Football

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Eric has a classic football that is made of 32 pieces of leather: 12 black pentagons and 20 white hexagons. Each pentagon adjoins 5 hexagons and each hexagon adjoins 3 pentagons and 3 hexagons. Eric drew a polygon (i.e. a closed line without intersections) along the edges of the pieces. The polygon divided the ball into two parts and Eric painted one of them green.

Eric's football

He is curious if given a description of the polygon you are able to compute the number of black, white and green pieces?


Write a program that:

  • reads the description of a polygon,
  • computes the number of black, white and green pieces,
  • writes the result.

Contest note: the first accepted solution will be awarded with the original football used for preparing the problem, signed by Eric, the author of the problem!

SPOJ note: the first accepted solution will be awarded some other sphere, without anybody's signatures, sent in PNG format to the author's email address [the offer is invalid, the sphere has already been presented to Robin Nittka, University of Ulm, Germany].


The input begins with the integer t, the number of test cases. Then t test cases follow.

For each test case, the first line of the input contains one integer n being the number of vertices of the polygon. The second line of the input contains n integers a1, a2,..., an separated by single spaces. Integer ai (equal 1 or 2) is the number of green pieces adjoining the i-th vertex of the polygon. The side of the polygon connecting the n-th and the first vertex always lies between two hexagons.


For each test case the first and only line of the output contains three integers b, w and g - the numbers of black, white and green pieces respectively.


Sample input:
1 2 1 2 1 2 1 1 1 2 2 1 1 1 1 2 2 2 1 1 1 

Sample output:
11 15 6 

Added by:adrian
Time limit:0.100s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Resource:ACM Central European Programming Contest, Warsaw 2003 (E. Kopczynski)