Fractal Cake

Fyodor celebrates his birthday today. Before the guests arrive he decorates a cake with chocolate cream in a special way.

At the start the cake is a square split into 4 equal white square cells — a $2 \times 2$ grid.

Fyodor calls the following sequence of steps a fractalization:

1. Group all current cells into non-overlapping $2 \times 2$ groups, so that no cell is left ungrouped.
2. Split every cell into 4 equal cells, so each $2 \times 2$ group becomes a $4 \times 4$ group. Every new cell keeps the color of the cell it was split from.
3. Fill the 4 central cells (the middle $2 \times 2$) of each $4 \times 4$ group with chocolate.

Fyodor does not stop after one fractalization: he repeats it N times, even when he needs a microscope. The picture below shows the initial cake, the result after the first fractalization, and the cake after the fifth fractalization:

After N fractalizations the cake is a $2^{N+1} \times 2^{N+1}$ grid of cells. Fyodor wants a program that quickly shows the pattern of a chosen rectangular part of the cake.

A single line contains five non-negative integers N, R1, R2, C1, C2:

• N — the number of fractalization iterations ($N < 20$).
• R1, R2 — the first and last row of the part.
• C1, C2 — the first and last column of the part.

Rows and columns are numbered from 0. The following restrictions hold: $R1 \le R2$, $C1 \le C2$; $0 \le R2 - R1 < 100$ and $0 \le C2 - C1 < 100$; $0 \le R1, R2, C1, C2 < 2^{N+1}$.

Print $R2 - R1 + 1$ lines, each containing $C2 - C1 + 1$ characters. Each character corresponds to one cell: it is 1 if the cell is filled with chocolate and 0 otherwise.