  We apply a bootstrap procedure to two-loop MHV amplitudes in planar N=4
super-Yang-Mills theory. We argue that the mathematically most complicated part
(the $\Lambda^2 B_2$ coproduct component) of the n-particle amplitude is
uniquely determined by a simple cluster algebra property together with a few
physical constraints (dihedral symmetry, analytic structure, supersymmetry, and
well-defined collinear limits). We present a concise, closed-form expression
which manifests these properties for all n.
