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Suppose that for each $1\\le j_{1}<j_{2}\\le d$ there exists $i\\in\\Lambda$ so that $|r_{i,j_{1}}|\\ne|r_{i,j_{2}}|$, and that for each $1\\le j\\le d$ the IFS $\\left\\{ t\\rightarrow r_{i,j}t+a_{i,j}\\right\\} _{i\\in\\Lambda}$ on the real line is exponentially separated. 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