Coprime Grid

The input and output sizes can be very large, so fast I/O is recommended.

For a positive integer $N$, consider a $5 \times 2N$ grid. Each cell must contain one integer among $1,2,\cdots,10N$, and every integer must be used exactly once.

Consider a pair of cells sharing an edge. If the two written integers are coprime, this pair is called a good pair. Otherwise it is called a bad pair.

You are given $T$ values $N_1,N_2,\cdots,N_T$. For each $N_i$, output one $5 \times 2N_i$ grid. Fewer bad pairs give a higher score.

The input is given in the following format.

$T$ $N_1\ N_2\ \cdots\ N_T$

For each test case $i$ ($1 \leq i \leq T$), print $5$ lines. Each line must contain $2N_i$ integers separated by spaces.

The printed $5 \times 2N_i$ integers for that test case must be a permutation of $1,2,\cdots,10N_i$.

• $1 \leq T \leq 1000$.
• $1 \leq N_i \leq 10^5$ ($1 \leq i \leq T$).
• $N_1+N_2+\cdots+N_T \leq 10^6$.

For each test case $i$, if the printed grid is not a permutation of $1,2,\cdots,10N_i$, define $F_i=0$.

Otherwise, let $B_i$ be the number of bad pairs, and define $F_i$ as follows.

Define $w_N$ as follows.

The score of the first subtask is as follows.

For the second subtask, the score of each data file is as follows.

The score of the second subtask is the minimum score among all data files.