Iskander the Baker is decorating a huge cake, covering the rectangular surface of the cake with frosting. For this purpose, he mixes frost- ing 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 A1, A2, . . . , An centimeters, and horizontal stripes of height B1, B2, . . . , Bn centimeters, for some positive integer n. These stripes split the cake surface into n × n rectangles. The intersection of vertical stripe i and horizontal stripe j has color number (i + j) mod 3 for all 1 ≤ i,j ≤ n. To prepare the frosting, Iskan- der wants to know the total surface in square centimeters to be colored for each of the three colors, and asks for your help. Input The input file contains several test cases, each of them as described below. The input consists of the following integers: • on the first line: the integer n, • on the second line: the values of A1, . . . , An, n integers separated with single spaces, • on the third line: the values of B1, . . . , Bn, n integers separated with single spaces. Limits The input satisfies 3 ≤ n ≤ 100000 and 1 ≤ A1,...,An,B1,...,Bn ≤ 10000. Output For each test case, the output must follow the description below. The output should consist of three integers separated with single spaces, representing the total area for each color 0, 1, and 2. Sample Input 3 111 111
2/2 7 6245114 2514234 Sample Output 333 155 131 197