About the taraweeh

As sallamuallay kum, i wanna ask that i have read a hadith which says who ever pray taraweeh behind the imam with complete witra. It is as if he prayed all night. But i wanna know that i pray taraweeh behind the imam and don't pray witra and come back home read quran and watch some islamic lectures and at night about 3-4am just before 30min in suhoor i pray 4 rakkat and 3 rakah witar as i have heard that we should complete our daily prayers with witra as the last. So do i get the same reward as praying taraweeh and witra behind imam ???