In 1954, Hans Peter Luhn invented a simple checksum method that can be used to detect simple errors in various identification numbers. Today this method, known as Luhn's checksum, is used to check for the validity of credit card numbers, Canadian social insurance numbers, and numerous others C i-0 Xi-101, where x, e {0, . . . , 9} for all 0 is n. In other words, XnX,-1 . . . X0 onsider a number x = is the sequence of x's decimal digits. For the numberx 932, for example, we have n-2, x2-9 x,-3, and x,-2. To calculate Luhn's checksum, we transform the sequence x x,, xn-i., Xo into another sequence y-(yn, yn-i , . . . , yo) defined as x fi is even 2x ifi is odd for all 0 defining i