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What is the minimum value of qq such that there are always three elements xmx_m, xnx_n, xpx_p of the set A={x1,x2,,xq1,xq}{1;2;;1233;1234}\mathbb A = \{x_1, x_2, \cdots, x_{q - 1}, x_q\} \in \{1; 2; \cdots; 1233; 1234\} such that xn22xpxm<xp2+xm2<xn2+2xpxmx_n^2 - 2x_px_m < x_p^2 + x_m^2 < x_n^2 + 2x_px_m (with every possible combination of the set A\mathbb A)?

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