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Let $n$ be any positive integer, and $X_n$ be the $n+1$ dimensional smooth complex affine cluster variety associated to the $A_n$ quiver (with $n$ unfrozen vertices and one frozen vertex). We prove that $X_n$ is self-mirror in the sense of homological mirror symmetry.  This is a first step towards understanding the Goncharov-Shen mirror symmetry conjecture for local system on decorated surfaces. We construct an 'closed cover' of A-side skeleton that is mirror to Zariski descent on the B-side.