Dormitory Password Recovery

This is an interactive problem.

Hanbyeol and Woobin were assigned to the same dormitory room. Woobin did not want to share a room with Hanbyeol, so before Hanbyeol moved in, Woobin installed a password lock on the door. To open the lock, you must find $N$ integers $x_1, x_2, \cdots, x_N$ that satisfy $0 \leq x_i < 998\,244\,353$. Woobin provides the following function to test your programming skill. You choose $N$ integers $a_1, a_2, \cdots, a_N$ and learn the value $f(a_1, a_2, \cdots, a_N)$.

Let $\mathbb{M}$ be the set of integers from 0 up to, but not including, 998244353. The function $f: \mathbb{M} \times \cdots \times \mathbb{M} \rightarrow \mathbb{M}$ is defined as

$f(a_1, a_2, \cdots, a_N) = (a_1 x_1 + a_2 x_2 + \cdots + a_N x_N) \bmod 998\,244\,353$

You may use the function at most $N$ times. Across all uses, the arguments $a_1, \cdots, a_N$ must all be different. That is, if you use the function $k$ times, all $kN$ arguments must be distinct.

Recover the password and surprise Woobin.

$2 \leq N \leq 2500$

Your program must flush the output buffer immediately after printing anything. Flush methods by language:

• C: fflush(stdout)
• C++: std::cout.flush()
• Python: sys.stdout.flush()
• Java: System.out.flush()
• For other languages, check the documentation of that language.