The Universal Product Code (UPC) is a 12-digit number found on products that enables them to be identified by electronic scanning devices. The first six digits identify the country of origin and the manufacturer, the next five digits indicate the product, and the last digit is a check digit. If the first eleven digits of a UPC are a1, a2,…, a11, then the check digit a12 is chosen so that 0 ≤ a12 < 10 and 3a1 + a2 + 3a3 + a4 + • • • + 3a11 + a12 ≡ 0 (mod 10). Find the correct check digit for the product that has 0 70330 20118 as its first 11 digits.
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