Twenty one days of travel. Do I need a twenty one day JR pass?

1) arrive in KIX. Train to Osaka overnight.
2) train to Tokyo x 4 nights
3) train to Nagano -> Shiga Kogen to ski x 1 night.
4) 1 night in Nozawa onsen to see snow monkey and town.
5) morning train to Tokyo. 1 night
To explore Ginza area. 6) train to Kyoto. X 2 nights
7) train to Nara. 1 night to see mountain burning.
8) trains to Mt. koya. 1 night
9) trains to Osaka. 3 nights.
10) train to Hiroshima. 2 nights
Inclides train to Miyajima and Bunny island.
11) train to Osaka. 2 nights.
Will we need a 21 day pass or a 14 day pas with supplememtal tickets.