Do Not Believe T's Story

For every judge testcase, your submitted program is run twice in two independent fresh processes. The only information passed between the runs is one integer printed by the first run.

T claims that everything they say can be trusted. You have discovered that some of T's statements are lies.

The statements are numbered from $1$ through $1\,000\,000$, and exactly $10\,000$ of them are lies. Let $S$ be the set of their numbers.

After seeing $S$, you want to warn Miku. You may communicate only one integer $X$ satisfying

On the first run, your program receives $S$ and prints $X$. The second run starts as a separate fresh process and retains no state, files, or memory about $S$. It receives only the value $X$ printed by the first run and prints the statement numbers it considers lies.

Every number printed by the second run must belong to $S$. Printing even one number outside $S$ results in a wrong answer. Help Miku identify as many lies as possible in every testcase.

Scoring

Assume that no incorrect statement number is printed. Your score is determined by the minimum value of $M$ over every judge testcase.

A solution with $M\geq9$ receives $100$ points. Printing a number that is not a lie, or producing malformed output, results in a wrong answer.

Your program is run twice for each judge testcase. The first integer of the input identifies the run.

The first run receives:

$1$ $10\,000$ $S_1\ S_2\ \cdots\ S_{10\,000}$

On the first run, print one integer $X$:

$X$

It must satisfy $0\leq X\leq2^{64}-1$. Any additional token other than surrounding whitespace results in a wrong answer.

• $|S|=10\,000$.
• $1\leq s\leq1\,000\,000$ for every $s\in S$.