Consider language $L$ over alphabet $=\{0,1\}$ :

$L=\{win{}^{**}$:${\displaystyle \underset{i=1}{\overset{|w|}{}}}(1-w_i)=2{\displaystyle \underset{i=1}{\overset{|w|}{}}}{w}_i\}.$

Earning full credit on this problem requires completing the following two $(2)$ parts.

$($i$)$ Prove or disprove $L$ is decidable.

$($ii$)$ Prove or disprove $L$ is Turing recognizable.