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In particular, we prove that if an IET $(J,T)$ is ergodic (relative to the Lebesgue measure $\\lam$), then the equality \\[ \\liminf_{n\\to\\infty}\\limits n |T^n(x)-y|=0 \\tag{A1} \\] holds for $\\lam\\ttimes\\lam$-a. a. $(x,y)\\in J^2$. The ergodicity assumption is essential: the result does not extend to all minimal IETs. 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