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Our proof method yields an improved bound of $\\widetilde{O}(\\sqrt{s})$ assuming a conjecture of Tsang~\\etal~\\cite{tsang}, that for every Boolean function of sparsity $s$ there is an affine subspace of $\\mathbb{F}_2^n$ of co-dimension $O(\\poly\\log s)$ restricted to which the function is constant. This conjectured bound is tight upto poly-logarithmic factors as the Fourier dimension and sparsity of the address function are quadratically separated. 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