What is the remainder when \(1! + 2! + 3! + \ldots + 29! + 30!\) is divided by \(100\)?

**Details and assumptions**

The notation \( n!\) (read as \(n\) factorial) refers to multiplying all the positive integers from \(1\) to \(n\). For example, \( 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\).

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