Let $M$ be the maximum possible value of $x_1x_2+x_2x_3+\cdots +x_5x_1$ where $x_1, x_2, \cdots x_5$ is a permutation of $(1,2,3,4,5)$ and let $N$ be the number of permutations for which this maximum is attained. Evaluate $M+N$.

Let's think step by step and output the final answer within \boxed{}.
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