Endless Candy Party

Mirko loves parties, so he decided to throw them for his friends without end. He set up $N$ tables and put candy on every one of them: table $i$ holds $b_i$ candies. On the first day he invites one friend to each table, on the second day two friends to each table, on the third day three, and in general on day $k$ he invites $k$ friends to each table.

When the friends walk in, $k$ of them sit down at every table and split that table's candy equally among themselves, throwing away the candy that does not divide evenly. A person sitting at table $i$ on day $k$ therefore receives $\lfloor b_i / k \rfloor$ candies. After the split, a table only mingles with tables whose people received the same amount, so the tables fall into groups by the amount of candy per person.

For every $s$ from $1$ to $N$, Mirko wants to know the earliest day on which some group holds exactly $s$ tables. Write a program that reports all $N$ answers.

Mirko refills every table to its original amount before each party starts, and everyone from one party leaves before the next one begins.

The first line contains the integer $N$, the number of tables. ($1 \le N \le 100$)

The second line contains the integers $b_1, b_2, \dots, b_N$ separated by spaces, where $b_i$ is the number of candies on table $i$. ($1 \le b_i \le 10^8$)

Print $N$ lines. Line $s$ contains the number of the earliest day on which a group of exactly $s$ tables mingles together, or $-1$ if that day never comes.

In the first example, no two tables give the same amount per person on day 1, so every table forms a group of one and the answer for size 1 is 1. On day 2, tables 1 and 2 both give 5 candies per person and mingle, so the answer for size 2 is 2. On day 3, tables 1, 2 and 3 all give 3 candies per person. On day 6, tables 1 to 4 all give 1 candy per person. On day 12, every table gives 0 candies per person, so all five tables become one group.

In the second example, all tables hold the same amount of candy, so the amount per person is always the same. A group smaller than 3 never appears.