Description

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.

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 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

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

21
1 2 1 2 1 2 1 1 1 2 2 1 1 1 1 2 2 2 1 1 1

11 15 6

Source

Central Europe 2003