Tris

You are given some domino-like pieces. The following types of pieces are possible:

Note that there are only four types, and you may rotate and reflect any piece for further use. You want to place all the pieces in a matrix of size at most $800 \times 800$ so that you get a single non-self-touching cycle. Formally, this means:

• All pieces must fully fit in the matrix and be aligned with the grid.
• No two pieces may overlap.
• If a certain matrix cell is occupied by a piece, then exactly two of its four neighbours must also be occupied.
• All occupied cells are connected. In other words, you can travel from any occupied cell to any other occupied cell by only moving to adjacent occupied cells.
• The "interior" of the cycle must be a single 4-connected area.

The input consists of a single line containing four integers: the number of pieces of each type (in the order they are shown in the image). It is guaranteed that each number is at least 2 and at most 100, and that at least one valid answer exists.

The first line of output must contain two integers $N$ and $M$ ($N, M \le 800$) denoting the number of rows and columns in your matrix. The next lines must describe the matrix in the following format:

• The matrix must contain integers between 0 and the total number of pieces, inclusive.
• Cells occupied by the same piece must have the same value.
• Cells occupied by different pieces must have different values.
• Cells that are not occupied by any piece must have the value 0.

If there are several valid answers, print any one of them.