Do you really like 11 so much?

A number is formed using the digits 2,4,72,4,7 exactly once, and using as many zeroes as required for adjustment.

Then SS be the set of remainders which can NOT be obtained on dividing the number by 1111 . Find the sum of all elements of SS

Details and assumptions :-

\bullet\quad A set contains each element exactly once, no repetitions.

S\bullet \quad S only contains some integers kik_i in the range 0ki100\leq k_i \leq 10, as remainder is , by definition, 0remainder<divisor0\leq remainder < divisor.

\bullet \quad You are expected to find the sum of all elements in SS, that is the remainders which can't be obtained by dividing the number by 1111.

\bullet\quad The number 24702470 is a a valid number for consideration, and so is 204007204007 and all others which contain only the digits 2,4,7,02,4,7,0 and 2,4,72,4,7 are exactly once. (Thus, 22472247 is not a valid number)

This is a part of set 11≡ awesome (mod remainders)


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