The following image depicts the layers of a $5\times5\times5$ cube. Using 3-dimensional thinking, can you find the way out of the cube?
1. Crossword (blue squares)
7. Physical or online locations
10. Caesar's planet
13. Venomous snake
14. Milan cathedral
15. Plantagenets and Lancasters
18. Avoid, escape
19. Slim, smooth
1. Dumas character
2. Economic resource
3. Levels or makers of knots
10. Shy, fearful
11. Fictional Vietnam War veteran
12. Texas battle site
15. Clarinet, saxophone and others
16. A grave digger's tool or suit
17. Creep around
1. Place where bridehood ends
2. A hectare is 2.5 –
4. Man in Paris
5. Music sometimes played with one note
6. Use a rubber
7. Dr Pepper and Mountain Dew, for example
8. Recurring theme, motif
9. Share in a company
2. Cryptic (yellow squares)
7. Sticky substance from messy rupture (5)
8. No credit for one surrounded by debt (5)
11. Country to not get any introductions (5)
12. Small instrument making piece of furniture (5)
5. Instruments for speakers of falsehoods called out (5)
6. Plant lit up, put out (5)
9. Troops destroyed, having lost second city (5)
10. Some pig looks for place to live (5)
1. Piece of shiny long-lasting material (5)
2. Car infested with insects (5)
3. Airline is flying late after opening day (5)
4. Big boy misses opening of Golden Ox (5)
3. Statue View (red numbers)
Insert the eight given 3D-tromino pieces (seven L-shaped, one I-shaped) into the cube. Pieces may be rotated in any direction. (Remember, these are 3D pieces so use the Z-axis as well!) The resulting space must satisfy the rules1 of Statue View:
- Pieces cannot be adjacent to each other, but may touch at a corner.
- All unoccupied cells must be (orthogonally) connected.
- Any cells with red numbers must be unoccupied. These numbers give the total lengths of the runs of occupied cells starting immediately adjacent to the number, and extending outwards from it.
1 This puzzle type was invented by Deusovi and introduced in Statue View: Tetrominoes.
Starting from the central square and treating occupied cells as walls, find the shortest way out.
The final answer is what was required in order to escape the cube (two words).