## MOG Training #6## Ended |

Iskander the Baker is decorating a huge cake, covering the
rectangular surface of the cake with frosting. For this purpose, he
mixes frosting sugar with lemon juice and food coloring, in order to
produce three kinds of frosting: yellow, pink, and white. These colors
are identified by the numbers 0 for yellow, 1 for pink, and 2 for white.

To
obtain a nice pattern, he partitions the cake surface into vertical
stripes of width $A_1, A_2, \dots, A_n$ centimeters, and horizontal
stripes of height $B_1, B_2, \dots, B_n$ centimeters, for some positive
integer $n$. These stripes split the cake surface into $n\times n$
rectangles. The intersection of vertical stripe $i$ and horizontal
stripe $j$ has color number $(i+j) \bmod 3$ for all $1 \leq i,j \leq n$.
To prepare the frosting, Iskander wants to know the total surface in
square centimeters to be colored for each of the three colors, and asks
for your help.

The input consists of the following integers:

- on the first line: the integer $n$,
- on the second line: the values of $A_1,\dots,A_n$, $n$ integers separated with single spaces,
- on the third line: the values of $B_1,\dots,B_n$, $n$ integers separated with single spaces.

Limits

The input satisfies $3\leq n \leq 100\,000$ and

$1 \leq A_1,\ldots,A_n,B_1,\ldots,B_n \leq 10\,000$.

The output should consist of three integers separated with single spaces, representing the total area for each color 0, 1, and 2.

Input

3
1 1 1
1 1 1

Output

3 3 3

Input

7
6 2 4 5 1 1 4
2 5 1 4 2 3 4

Output

155 131 197