One proposed explanation for the importance of remainder problems inChinese mathematics is the application to determining astronomical events. The Chi-nese recognized three major cycles in their calendars: a solar year cycle of 365 days, alunar cycle of 28 days, and an artificial cycle of 60 days. Suppose we want to determinethe time elapsed between from the common beginning of the cycles to an event thatoccurs on a day which is the 82nd day of the solar cycle, the 11th day of the lunarcycle, and the 7th day of the 60-day cycle. Then this amounts to finding x such thatx 82(mod 365), x 11(mod 28), x 7(mod 60).Determine the smallest such x.