2023 Fermat Problem 23

For each positive integer n, define s(n) to equal the sum of the digits of n. For example, s(2023) = 2+0+2+3. The number of integers n with 100 \le n \le 999 and 7 \le s(n) \le 11 is S. What is the integer formed by the rightmost two digits of S?

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Full credit to this problem is given to the CEMC, you may view all Fermat contests here.