$n!$ means $n\times (n-1)\times \cdots \times 3\times 2\times 1$.

For example, $10!=10\times 9\times \cdots \times 3\times 2\times 1=3628800$,
and the sum of the digits in the number $10!$ is $3+6+2+8+8+0+0=27$.

Find the sum of the digits in the number $100!$.