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The coexistence of $^{26}{\\rm Al}$-rich and $^{26}{\\rm Al}$-poor calcium--aluminum-rich inclusions indicates that a direct injection of $^{26}{\\rm Al}$-rich materials from a nearby core-collapse supernova should occur in the first $10^5$ years of the solar system. Therefore, at least one core-collapse supernova should occur within the duration of star formation in the Sun's birth cluster. 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