Can I split 2020-2021 school tuition between the two years returns if it is paid at once in full?

I paid tuition fee for my child in full in September 2020 for the 2020-2021 school year while it was possible to split it into multiple payments in 2020 and 2021. Can I still claim Child and Dependent Care Credit in proportion between 2020 and 2021 assuming that out of 10 months school year 4/10 of the payment (Sep, Oct, Nov, Dec) covers 2020 and  6/10 of it (Jan, Feb, Mar, Apr, May, Jun) goes to 2021?