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Fix $n\geq6$. Consider the set $C$ of binary strings $x_1x_2...x_n$ of length n such that the bits satisfy the following set of equalities, all modulo 2: $x_i + x_{i+1} + x_i+2 = 0$ for all $1\leq i\leq n-2, x_{n-1} + x_n + x_1 = 0$, and $x_n + x_1 + x_2 = 0$. What is the size of set $C$?

(A) $1$ for all $n\geq6$

(B) $4$ for all $n\geq6$

(C) $0$ for all $n\geq6$

(D) If $n \geq6$ is divisible by $3$ then $|C| = 1$. If $n\geq 6$ is not divisible by $3$ the $|C| = 4$

(E) If $n \geq6$ is divisible by $3$ then $|C| = 4$. If $n\geq 6$ is not divisible by $3$ the $|C| =14$
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