Problem $7(5$ marks$)$ Let us define the period of a string $s=c_1{c}_2{c}_{3}dots{c}_n$ as the smallest positive $k>0$ such that removing the first $k$ characters of $s$ results into the same string as removing its last $k$ characters, i$.$e$.)=(c_{1}dots{c}_{(n-k)}.$ For example, the period of aabaacaabaa is $6-$removing the first $6$ characters gives us aabaa, which is also what we get by removing the last $6$ characters. You may also check that $6$ is lowest such $k$ for which this holds here. Simitarly, the period of abcabcab is $3$ and the period of abcde is $5.$

Describe an $O(n)$ algorithm $($in words, no pseudocode$)$ to compute the period of a string of length $n.$