Solution
If $$$n$$$ is a perfect square number, we find that the square dyeing scheme is always optimal.The answer is $$$4\sqrt{n}$$$.
Otherwise,if $$$n-\lfloor \sqrt{n} \rfloor ^2 \leq \lfloor \sqrt{n} \rfloor$$$,the answer is $$$4\lfloor \sqrt{n} \rfloor+2$$$.Otherwise the answer is $$$4\lfloor \sqrt{n} \rfloor+4$$$.
Solution
If $$$n$$$ is odd,we can traverse all cells, which is a simple situation.
If $$$n$$$ is even,we can skip one of $$$(1,2) (1,4) (1,6)...(1,n),(2,1),(2,3),(2,5)...(2,n-1)$$$.If there is a duplicate number, skip it. Otherwise, skip the maximum number.
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