Take the L

Dadas and Lunarlity play a game on a $2 \times N$ board with all cells initially present. Dadas moves first, and the players alternate turns.

On each turn, the current player must take three remaining cells forming an L shape. An L shape consists of three of the four cells in a $2 \times 2$ region formed by two consecutive columns. All four rotations are allowed. The fourth, unselected cell may already have been taken.

A cell that has been taken cannot be taken again. A player who has no legal L shape to take on their turn loses.

Determine whether Dadas can win when both players play optimally.

An example move for $N=6$: take the three yellow cells.

The input is given in the following format:

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

For each test case, print YES if Dadas can win, or NO otherwise, on a separate line.

• $1 \le T \le 1000$.
• $1 \le N \le 2000$.
• The sum of $N$ over all test cases is at most .