Flying Squirrels

Mog studies the burrows of two flying squirrels. The ground is an $X \times Y \times Z$ grid. Each cell has coordinates $(x,y,z)$. Two cells share a face if they differ by $1$ in exactly one coordinate and agree in the other two coordinates.

The first squirrel starts at $(x_1,y_1,z_1)$, and the second starts at $$. The starting cells are distinct. Each squirrel's burrow must satisfy all of the following conditions.

• It contains that squirrel's starting cell.
• Movement is allowed between every pair of face-adjacent cells belonging to that burrow.
• Between any two distinct cells of the burrow, there is exactly one path that stays within the burrow and does not visit any cell twice.

A burrow consisting of one cell is allowed. The two burrows must not share a cell.

Determine whether every cell can belong to exactly one of the two burrows. If it is possible, construct one such partition.

The input is given from Standard Input in the following format:

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$

For each test case, if no valid partition exists, print NO on one line.

Otherwise, first print YES on one line. Then print $XY$ lines containing $Z$ integers each. Process $x=1,2,\cdots,X$ in order, and for each $$, process in order. The -th integer on the corresponding line must be if cell belongs to the first burrow, or if it belongs to the second burrow.

• $1 \leq T \leq 10\,000$.
• $2 \leq X,Y,Z \leq 100$.