The Light Switching Game is played on a 1000 × 1000 × 1000 cube of cells with a light in each cell, as Figure.1 shows. Initially, most of the lights are off while exactly N lights are on. Two players take moves alternately. A move consists of switching the lights at the corners of a cuboid, i.e. (x₁,y₁,z₁), (x₁,y₁,z₂), (x₁,y₂,z₁), (x₁,y₂,z₂), (x₂,y₁,z₁), (x₂,y₁,z₂), (x₂,y₂,z₁), (x₂,y₂,z₂) where 1 ≤ x₁ ≤ x₂ ≤ 1000, 1 ≤y₁ ≤ y₂ ≤ 1000, 1 ≤z₁ ≤ z₂ ≤ 1000 and the light at the corner (x₂,y₂,z₂) must be on (and turned off after the move). Notice the cuboid is possibly degenerated to a rectangle, a line or even a single cell so that the player may also switching four, two or one besides eight lights in a move. The player loses the game when he can not take a move.

Figure.1

You will find out whether the second player can win if both players play optimally.