Problem Statement

There is a permutation $P = (P_1, P_2, \cdots,P_{N})$ of $(1, 2, \cdots, N)$ with $N$ elements. $N$ is a prime number. You are given $N$, but $P$ is not given and is kept hidden by the judge.

You can send the following query to the judge.

・Choose integers $i, j (i \neq j)$ between $1$ and $N$, inclusive. If there exists an integer $k$ such that $P_i + P_j = P_k$, you are given $k$; otherwise, you are given $-1$.

You can use this query up to $3N$ times. Find $P$.

Solve $T$ test cases.

Constraints

・$1 \leq T$

・$5 \leq N$

・$N$ is a prime number

・$P$ is a permutation of $(1, 2, \cdots, N)$

・$P$ is determined before the interaction and is fixed

・All inputs are integers

・The sum of $N$ over the test cases is at most $10001$

Input and Output

First, $T$ is given by the judge. After this, the following interaction is performed $T$ times.

$T$

First, at the beginning of each interaction, $N$ is given.

$N$

After that, you can send queries in the following format up to $3N$ times. They must satisfy $1 \leq i, j \leq N, i \neq j$.

$1$ $i$ $j$

The judge responds with the answer to the query. If there exists an integer $k$ such that $P_i + P_j = P_k$, $k$ is given; otherwise, $-1$ is given.

$k$

When outputting your answer, print it as follows. If this is the $T$-th time, terminate your program immediately.

$2$ $P_1$ $P_2$ $\cdots$ $P_N$