Comedy's Not Omnipotent

This is an interactive problem.

Vim, Emacs, and Nano are playing a guessing game. Vim secretly told Nano a random binary sequence $\\{a\_i\\}$ of length $n$. Emacs can query Nano with a set of indices $I \subseteq \\{1, 2, \ldots, n\\}$. Nano will reply with $\sum\_{i \in I} a\_i$. Could you please help Emacs find $\\{a\_i\\}$ in less than $n/2$ queries? Additionally, the total size of the sets in all queries must not be greater than $3n$.

The size $n = 10^5$ in all tests. The example with $n = 4$ shows the format but will not be tested.

There are at most $50$ tests in this problem. The tests were generated randomly, but are fixed in advance. In each test, every binary sequence of length $n$ had the probability of $1/2^n$ to be generated.