number theory - How many zeros are there in $1 times 2^2 times 3^3 times cdots times 100^{100}$?

How many zeros are there at the end of $1 \times 2^2 \times 3^3 \times \cdots \times 100^{100}$ ?

I tried it by grouping all the $2$'s and $5$'s and $5$'s and $6$'s but cant get my answer...