Q48

Consider a computer system with $57$-bit virtual addressing using multi-level tree-structured page tables with $\mathrm{L}$ levels for virtual to physical address translation. The page size is $4 \mathrm{~KB}(1 \mathrm{~KB}=1024 \mathrm{~B})$ and a page table entry at any of the levels occupies $8$ bytes. The value of $\mathrm{L}$ is ______________.