Goal
Takuzu (aka 'Binary Sudoku' or 'Binairo') is a variant of Sudoku that only allows the numbers 0 and 1. The following three rules must be met for a valid solution:
1. Each row and column must contain an equal number of 0s and 1s (e.g. 5 of each for a 10x10 grid).
2. No row or column may contain a sequence of three or more repeating digits (e.g. 1 1 0 is valid but 1 1 1 is invalid) (Hint: you can solve this 'Easy mode' puzzle with just this rule)
3. No rows (or columns) can be duplicates of other rows (or columns).
Given an integer n and an incomplete nxn binary grid of 0s and 1s, with . symbols for unknown values, complete the grid by replacing all the unknown values with 0s and 1s, obeying the required rules.
There will only be one valid solution.
Hard version: https://www.codingame.com/training/hard/takuzu-solver (Hint: you will need to include a backtracking algorithm and use all three rules)
Input
Line 1 : An integer n, the size of the grid (always even)
Next n lines : A row of n characters: 0, 1 or . (for unknown values)
Output
n lines : The completed board, with all . replaced with valid 0s and 1s, following the rules.
Constraints
4 < n < 16
n is even
All boards have a single valid solution
All boards can be solved using rule 2 alone (easy mode).
Example
Input
6
.0...1
0.11..
..1..0
.1...0
....1.
11.0.0
Output
100101
001101
011010
110100
001011
110010
