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We study the degeneracy of non-Archimedean analytic maps from k into $X\\setminus \\cup_{i=1}^nD_i$ under various geometric conditions. When X is a rational ruled surface and D_1 and D_2 are ample, we obtain a necessary and sufficient condition such that there is no non-Archimedean analytic map from k into $X\\setminus D_1 \\cup D_2$. 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