Board Game

A friend recently gave you a board game as a gift. It is like Tsirkus, but cyclic.

The board has $N$ cells numbered $1, \ldots, N$, and cell $N$ is followed by cell $1$. Each cell $i$ has an integer $a_i$ written on it.

• If $a_i = 0$, the player throws a six-sided die at cell $i$ and moves forward by the result.
• If $a_i \ne 0$, the player moves forward $a_i$ cells (backward if $a_i$ is negative).

The second rule repeats until the player lands on a cell with $0$ written on it. The player may also get stuck in an infinite cycle. The game starts at cell $1$, and $a_1 = 0$.

You suspect that some cells can never be reached. Write a program that finds which cells can be visited during the game.

The first line contains the number of cells $N$ ($1 \le N \le 1000$). The second line contains the space-separated integers $a_1, \ldots, a_N$ ($-N < a_i < N$, $a_1 = 0$).

Print a single line with $N$ space-separated numbers, each $0$ or $1$. The $i$-th number is $1$ if cell $i$ can be visited, and $0$ if it cannot.