Farhans Football

Problem code: ARFF

All submissions for this problem are available.

Farhan has a standard 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. Farhan 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 Farhan painted one of them green.

Football Explantion

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

Task

Write a program that:
  • reads the description of a polygon
  • computes the number of black, white and green pieces
  • writes the result


Input

The input has two test cases.

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.

Output

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.

Example

Sample input: 
21 
1 2 1 2 1 2 1 1 1 2 2 1 1 1 1 2 2 2 1 1 1 
21 
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 
11 15 6

Author: iamsurya
Date Added: 28-09-2010
Time Limit: 1 sec
Source Limit: 50000 Bytes
Languages: ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.0.0-8, CPP 4.3.2, CS2, D, ERL, F#, FORT, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TEXT, WSPC


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