Binario Grid Validator

Statement

Goal

Validate that the given grid is a valid Binario.

Binario, also called Binary Sudoku, is a puzzle where you have to fill a nxn grid with 1s and 0s while satisfying these three guidelines :
1 - For each row and column, half the digits are 1s and the other half are 0s.
2 - For each row and column, there can never be more than two consecutive ones or two consecutive zeros.
3 - No two rows can be identical. No two columns can be identical.

If the grid is valid, output VALID.
If the grid is invalid, output the lowest index to an invalid row or, if all rows are valid, the lowest index to an invalid column. Indexes of rows and columns are zero-based.

Input

Line 1 : An integer n giving the size of the grid (n x n)
Next n lines : The n space separated digits for each row of the grid (starting with row 0)

Output

VALID if the grid is valid, else the lowest index to an invalid row or, if all rows are valid, the lowest index to an invalid column. Indexes of rows and columns are zero-based.

Constraints

6 ≤ n ≤ 14
n is always even.
The grid only contains 1s and 0s. There are neither empty cells nor other characters.

Example

Input

6
1 0 0 1 0 1
0 1 0 1 1 0
1 0 1 0 0 1
0 1 1 0 0 1
1 0 0 1 1 0
0 1 1 0 1 0

Output

VALID

Game modes

Fastest, Shortest

Test cases

Test 1 - Valid Test

Input

6 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0

Output

VALID

Validator 1 - Valid Validator

Input

8 1 1 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 0 1

Output

VALID

Test 2 - Rule 1 row Test

Input

12 1 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0 1 0 1 1 0 1

Output

Validator 2 - Rule 1 row Validator

Input

14 0 1 1 0 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 1 0 1 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 0

Output

Test 3 - Rule 2 row Test

Input

8 1 1 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 0 1 0 1

Output

Validator 3 - Rule 2 row Validator

Input

10 1 0 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 0 1 0 1 1

Output

Test 4 - Rule 3 row Test

Input

10 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1

Output

Validator 4 - Rule 3 row Validator

Input

6 1 0 1 0 0 1 0 1 1 0 1 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0 1

Output

Test 5 - Rule 1 column Test

Input

12 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 0 1 0 0

Output

Validator 5 - Rule 1 column Validator

Input

14 0 1 1 0 0 1 1 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 1 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1

Output

Test 6 - Rule 2 column Test

Input

12 1 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0

Output

Validator 6 - Rule 2 column Validator

Input

10 1 1 0 0 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1

Output

Test 7 - Rule 3 column Test

Input

6 1 1 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1

Output

Validator 7 - Rule 3 column Validator

Input

8 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 0 1 1 0 1

Output

Solution language

Solution

Stub generator input

Comments

23 Comments

TheCrucial Unnamed CodinGamer

almost 4 years ago

please, provide testcase and not just validator for each rule considering both column and row. would be really helpfull

Adam798 Unnamed CodinGamer

That's a good idea. I added test cases for each rule for rows and columns. Hope it helps.

rafaelcs Unnamed CodinGamer

✅ Approved the contribution. Comment: This is a nice one for shortest and fastest clashes mod

I think the only thing missing, is a test case where n = 16

I don't know why I did not make one. But I think it is better at this point to change the constraints to 6<=n<=14 The size does not make a difference on the code.

AlkhilJohn. Unnamed CodinGamer

✅ Approved the contribution. Comment: Yep

lbadea1000 Unnamed CodinGamer

✅ Approved the contribution. Comment: It is fun

Is this too long for a clash of code ?

i dont think so, its a very straightforward algorithm, it mainly depends on the coder only, some could even bring a solution that solves for n <= 1000

CodinBot Unnamed CodinGamer

I hope you received enough feedback from the community to improve your contribution. Once you have made the necessary updates, publish your contribution!

TheEccentricDuck Unnamed CodinGamer

I just edited this puzzle to make the wording and grammar a little more concise and less ambiguous.

Very very innovative and original puzzle.

JonnyWhite Unnamed CodinGamer

Food job

codybumba Unnamed CodinGamer

Can you explain this part with an example - "Any two rows must be different by at least one digit, same for columns"?

It basicaly means that all rows (and columns) must be different (by at least one digit). An example of an invalid grid would be test case 4 where column 1 and 4 have all their corresponding digits equal so they don't differ by at least one digit. A valid example is Test 1 row 0 and 5 both start with 1001 but the last two digits are different so it is ok. I could rephrase into : "All rows must be different, same for columns. Two rows (or columns) are considered different if they differ by at least one digit." or something like that

Kapanion Unnamed CodinGamer

very nice. excellent for clash

nikelhaus Unnamed CodinGamer

it's more complicated than you think, nice puzzle though

Yeah I was wondering if this was too long for a clash of code. What the code needs to do is straightfoward, though.

Siddhu131 Unnamed CodinGamer

hmm

BartholomewIII Unnamed CodinGamer

about 4 years ago

I like this! A couple of things though: 1) State clearly that indexes are zero-based. 2) Change "true" to "valid" or something so some languages don't get an advantage in the shortest game mode.

Good ideas ! Puzzle is now changed to reflect this.

Hello everyone ! Here is my first contribution ! I know its not very original, but I wanted to try with something not too complicated first. Please give me your feedback, it will be greatly appreciated. Also, English is not my first language so please tell me if I made errors. Adam