Baseball Fans

There are $N$ people standing in a line. They are numbered from $1$ to $N$ from front to back.

Each person is a fan of one baseball team. Multiple people may support the same team, and different people may support different teams.

You may ask queries by calling the following function.

int query(vector<int> indices);

The vector indices must contain distinct person indices. The function returns the number of distinct teams supported by the people whose indices are contained in indices.

For example, if the selected people support teams $(A,A,C,B,C)$, then the return value is $3$.

Your goal is to determine the number of fans of each team using at most $1000$ queries.

Since the exact team names cannot be identified, the answer is judged as a multiset of team sizes. For example, if the true team sizes are $\{1,2,2,5\}$, then any permutation of these numbers is accepted.

This is a function-call problem.

Internally, each test case is given in the following format.

$N$ $T_1\ T_2\ \cdots\ T_N$

$T_i$ is the internal identifier of the team supported by person $i$. Your submitted program cannot read $T_i$ directly. The grader calls solve(N).

Do not print the answer directly to standard output. Instead, submit your answer by calling the following function exactly once.

void answer(vector<int> fan_counts);

The vector fan_counts must contain the number of fans of each team. The order does not matter.

• $1 \le N \le 100$.
• $1 \le T_i \le 1\,000\,000\,000$ ($1 \le i \le N$).
• query may be called at most $1000$ times.
• The size of indices passed to query must be between $1$ and $N$.
• All elements of indices must be distinct integers between $1$ and $N$.