I # Push the input-matrix yet again a # Convert all pieces to 1s with the is_alphabetic builtin © # Store this matrix of 1s/0s in variable `®` (without popping) ˜ # Flatten it ƶ # Multiply each value by its 1-based index Igä # Mold it back to a matrix matching the input: I # Push the input g # Pop and push the length (the amount of rows) ä # Split the matrix into that many equal-sized parts Δ # Loop until the result no longer changes: 2Fø0δ.ø} # Add a border of 0s around the matrix: 2F } # Loop 2 times: ø # Zip/transpose; swapping rows/columns δ # Map over each inner list: 0 .ø # Surround it with both a leading and trailing 0 2Fø€ü3} # Then split it into overlapping 3x3 blocks: 2F # Loop 2 times again: ø # Zip/transpose; swapping rows/columns again € # Map over each inner list again: ü3 # Split this list into overlapping triplets ®* # Multiply this matrix of 3x3 blocks and matrix `®` together, # so all 3x3 blocks at the 0-positions will become a block of 0s εεÅsyøÅs«à # Get the largest value from the horizontal/vertical cross of each # 3x3 block: εε # Nested map over each 3x3 block: Ås # Pop and push its middle row y # Push the 3x3 block again ø # Zip/transpose; swapping rows/columns Ås # Pop and push its middle rows as well (the middle column) « # Merge the middle row and column together to a single list à # Pop and push its maximum ] # Close the nested maps and flood-fill loop ˜ # Flatten the resulting flood-filled matrix 0K # Remove all 0s (the gaps) Ë # Check if all remaining values are the same, so we have a single island 

I # Push the input-matrix yet again a # Convert all pieces to 1s with the is_alphabetic builtin © # Store this matrix of 1s/0s in variable `®` (without popping) ˜ # Flatten it ƶ # Multiply each value by its 1-based index Igä # Mold it back to a matrix matching the input: I # Push the input g # Pop and push the length (the amount of rows) ä # Split the list into that many equal-sized parts Δ # Loop until the result no longer changes: 2Fø0δ.ø} # Add a border of 0s around the matrix: 2F } # Loop 2 times: ø # Zip/transpose; swapping rows/columns δ # Map over each inner list: 0 .ø # Surround it with both a leading and trailing 0 2Fø€ü3} # Then split it into overlapping 3x3 blocks: 2F # Loop 2 times again: ø # Zip/transpose; swapping rows/columns again € # Map over each inner list again: ü3 # Split this list into overlapping triplets ®* # Multiply this matrix of 3x3 blocks and matrix `®` together, # so all 3x3 blocks at the 0-positions will become a block of 0s εεÅsyøÅs«à # Get the largest value from the horizontal/vertical cross of each # 3x3 block: εε # Nested map over each 3x3 block: Ås # Pop and push its middle row y # Push the 3x3 block again ø # Zip/transpose; swapping rows/columns Ås # Pop and push its middle row as well (the middle column) « # Merge the middle row and column together to a single list à # Pop and push its maximum ] # Close the nested maps and flood-fill loop ˜ # Flatten the resulting flood-filled matrix 0K # Remove all 0s (the gaps) Ë # Check if all remaining values are the same, so we have a single island 

05AB1E, 71 bytes

ø«ε0¡ε€Sø€ËàyD¢P*]˜þPI˜áD¢4‹PIa©˜ƶIgäΔ2Fø0δ.ø}2Fø€ü3}®*εεÅsyøÅs«à]˜0KËP 

Try it online or verify all test cases.

ø # Zip/transpose; swapping rows/columns of the (implicit) input-matrix « # Merge this list of columns to the (implicit) input-list of rows ε # Map over each inner row/column: 0¡ # Split it on 0s (the gaps) ε # Map over each connected portion: €S # Split each 2-char string to a pair of characters ø # Zip/transpose; swapping rows/columns €Ë # Check for each inner list whether they're all the same à # Pop and get max, to check if this is truthy for either y # Push the current connected portion again D # Duplicate it ¢ # Pop both, and count how many times each portion occurs P # Take the product of these counts *  # Multiply the two checks together ] # Close the nested maps ˜ # Flatten the list of list of list of checks þ # Remove all empty strings by only keeping numbers # (occurs for leading/trailing gaps or two adjacent gaps in a row/column)   P # Check if everything was truthy by taking the product 

Try just this first step online or verify it for all test cases.

I # Push the input-matrix yet again a # Convert all pieces to 1s with the is_alphabetic builtin © # Store this matrix of 1s/0s in variable `®` (without popping) ˜ # Flatten it ƶ # Multiply each value by its 1-based index Igä # Mold it back to a matrix matching the input: I # Push the input g # Pop and push the length (the amount of rows) ä # Split the matrix into that many equal-sized parts Δ # Loop until the result no longer changes: 2Fø0δ.ø} # Add a border of 0s around the matrix: 2F } # Loop 2 times: ø # Zip/transpose; swapping rows/columns δ # Map over each inner list: 0 .ø # Surround it with both a leading and trailing 0 2Fø€ü3} # Then split it into overlapping 3x3 blocks: 2F # Loop 2 times again: ø # Zip/transpose; swapping rows/columns again € # Map over each inner list again: ü3 # Split this list into overlapping triplets ®* # Multiply this matrix of 3x3 blocks and matrix `®` together, # so all 3x3 blocks at the 0-positions will become a block of 0s εεÅsyøÅs«à # Get the largest value from the horizontal/vertical cross of each # 3x3 block: εε # Nested map over each 3x3 block: Ås # Pop and push its middle row y # Push the 3x3 block again ø # Zip/transpose; swapping rows/columns Ås # Pop and push its middle rows as well (the middle column) « # Merge the middle row and column together to a single list à # Pop and push its maximum ] # Close the nested maps and flood-fill loop ˜ # Flatten the resulting flood-filled matrix 0K # Remove all 0s Ë # Check if all remaining values are the same, so we have a single island 

Step 4: Combine all three checks of the previous step, and output the result:

05AB1E, 71 69 bytes

ø«ε0¡ε€Sø€ËàyD¢*]˜PI˜áD¢4‹PIa©˜ƶIgäΔ2Fø0δ.ø}2Fø€ü3}®*εεÅsyøÅs«à]˜0KËP 

Try it online or verify all test cases.

ø # Zip/transpose; swapping rows/columns of the (implicit) input-matrix « # Merge this list of columns to the (implicit) input-list of rows ε # Map over each inner row/column: 0¡ # Split it on 0s (the gaps) ε # Map over each connected portion: €S # Split each 2-char string to a pair of characters ø # Zip/transpose; swapping rows/columns €Ë # Check for each inner list whether they're all the same à # Pop and get the maximum, to check if this is truthy for either y # Push the current connected portion again D # Duplicate it ¢ # Pop both, and count how many times each piece occurs * # Multiply the earlier check to each count in the list ] # Close the nested maps ˜ # Flatten the list of list of list of checks P  # Check if everything was truthy by taking the product 

Try just this first step online or verify it for all test cases.

I # Push the input-matrix yet again a # Convert all pieces to 1s with the is_alphabetic builtin © # Store this matrix of 1s/0s in variable `®` (without popping) ˜ # Flatten it ƶ # Multiply each value by its 1-based index Igä # Mold it back to a matrix matching the input: I # Push the input g # Pop and push the length (the amount of rows) ä # Split the matrix into that many equal-sized parts Δ # Loop until the result no longer changes: 2Fø0δ.ø} # Add a border of 0s around the matrix: 2F } # Loop 2 times: ø # Zip/transpose; swapping rows/columns δ # Map over each inner list: 0 .ø # Surround it with both a leading and trailing 0 2Fø€ü3} # Then split it into overlapping 3x3 blocks: 2F # Loop 2 times again: ø # Zip/transpose; swapping rows/columns again € # Map over each inner list again: ü3 # Split this list into overlapping triplets ®* # Multiply this matrix of 3x3 blocks and matrix `®` together, # so all 3x3 blocks at the 0-positions will become a block of 0s εεÅsyøÅs«à # Get the largest value from the horizontal/vertical cross of each # 3x3 block: εε # Nested map over each 3x3 block: Ås #  Pop and push its middle row y #  Push the 3x3 block again ø #  Zip/transpose; swapping rows/columns Ås #  Pop and push its middle rows as well (the middle column) « #  Merge the middle row and column together to a single list à #  Pop and push its maximum ] # Close the nested maps and flood-fill loop ˜ # Flatten the resulting flood-filled matrix 0K # Remove all 0s (the gaps) Ë # Check if all remaining values are the same, so we have a single island 

Step 4: Combine all three checks of the previous steps, and output the result:

ø # Zip/transpose; swapping rows/columns of the (implicit) input-matrix « # Merge this list of columns to the (implicit) input-list of rows ε # Map over each inner row/column: 0¡ # Split it on 0s (the gaps) ε # Map over each connected portion: €S # Split each 2-char string to a pair of characters ø # Zip/transpose; swapping rows/columns €Ë # Check for each inner list whether they're all the same à # Pop and get max, to check if this is truthy for either y # Push the current connected portion again D # Duplicate it ¢ # Pop both, and count how many times each portion occurs P # Take the product of these counts * # Multiply the two checks together ] # Close the nested maps ˜ # Flatten the list of list of list of checks þ # Remove all empty strings by only keeping numbers # (occurs for leading/trailing gaps or two adjacent gaps in a row/column) P # And check if everything was truthy by taking the product 

I # Push the input-matrix again ˜ # Flatten it á # Remove all gaps by only keeping the letters D # Duplicate it ¢ # Pop both, and count how many times each piece occurs 4‹ # Check for each that it's smaller than 4 P # And check if everything was truthy by taking the product 

I # Push the input-matrix yet again a # Convert all pieces to 1s with the is_alphabetic builtin © # Store this matrix of 1s/0s in variable `®` (without popping) ˜ # Flatten it ƶ # Multiply each value by its 1-based index Igä # Mold it back to a matrix matching the input: I # Push the input g # Pop and push the length (the amount of rows) ä # Split the matrix into that many equal-sized parts Δ # Loop until the result no longer changes: 2Fø0δ.ø} # Add a border of 0s around the matrix: 2F } # Loop 2 times: ø # Zip/transpose; swapping rows/columns δ # Map over each inner list: 0 .ø # Surround it with both a leading and trailing 0 2Fø€ü3} # Then split it into overlapping 3x3 blocks: 2F # Loop 2 times again: ø # Zip/transpose; swapping rows/columns again € # Map over each inner list again: ü3 # Split this list into overlapping triplets ®* # Multiply each inner 3x3 block by the value at that position of matrix `®`, # so all 3x3 blocks at the 0-positions will become 0 εεÅsyøÅs«à # Get the largest value from the horizontal/vertical cross of each 3x3 block: εε # Nested map over each 3x3 block: Ås # Pop and push its middle row y # Push the 3x3 block again ø # Zip/transpose; swapping rows/columns Ås # Pop and push its middle rows as well (the middle column) « # Merge the middle row and column together to a single list à # Pop and push its maximum   ] # Close the nested maps and flood-fill loop ˜ # Flatten the resulting flood-filled matrix 0K # Remove all 0s Ë # And check if all remaining values are the same, so we have a single island 

ø # Zip/transpose; swapping rows/columns of the (implicit) input-matrix « # Merge this list of columns to the (implicit) input-list of rows ε # Map over each inner row/column: 0¡ # Split it on 0s (the gaps) ε # Map over each connected portion: €S # Split each 2-char string to a pair of characters ø # Zip/transpose; swapping rows/columns €Ë # Check for each inner list whether they're all the same à # Pop and get max, to check if this is truthy for either y # Push the current connected portion again D # Duplicate it ¢ # Pop both, and count how many times each portion occurs P # Take the product of these counts * # Multiply the two checks together ] # Close the nested maps ˜ # Flatten the list of list of list of checks þ # Remove all empty strings by only keeping numbers # (occurs for leading/trailing gaps or two adjacent gaps in a row/column) P # Check if everything was truthy by taking the product 

I # Push the input-matrix again ˜ # Flatten it á # Remove all gaps by only keeping the letters D # Duplicate it ¢ # Pop both, and count how many times each piece occurs 4‹ # Check for each that it's smaller than 4 P # Check if everything was truthy by taking the product 

I # Push the input-matrix yet again a # Convert all pieces to 1s with the is_alphabetic builtin © # Store this matrix of 1s/0s in variable `®` (without popping) ˜ # Flatten it ƶ # Multiply each value by its 1-based index Igä # Mold it back to a matrix matching the input: I # Push the input g # Pop and push the length (the amount of rows) ä # Split the matrix into that many equal-sized parts Δ # Loop until the result no longer changes: 2Fø0δ.ø} # Add a border of 0s around the matrix: 2F } # Loop 2 times: ø # Zip/transpose; swapping rows/columns δ # Map over each inner list: 0 .ø # Surround it with both a leading and trailing 0 2Fø€ü3} # Then split it into overlapping 3x3 blocks: 2F # Loop 2 times again: ø # Zip/transpose; swapping rows/columns again € # Map over each inner list again: ü3 # Split this list into overlapping triplets ®* # Multiply this matrix of 3x3 blocks and matrix `®` together, # so all 3x3 blocks at the 0-positions will become a block of 0s εεÅsyøÅs«à # Get the largest value from the horizontal/vertical cross of each  # 3x3 block: εε # Nested map over each 3x3 block: Ås # Pop and push its middle row y # Push the 3x3 block again ø # Zip/transpose; swapping rows/columns Ås # Pop and push its middle rows as well (the middle column) « # Merge the middle row and column together to a single list à # Pop and push its maximum ] # Close the nested maps and flood-fill loop ˜ # Flatten the resulting flood-filled matrix 0K # Remove all 0s Ë # Check if all remaining values are the same, so we have a single island