# Find PDA for CFL = {x#y | |x| = |y| and x ≠ y} [duplicate]

I am studying push down automata.

When I read a solution for showing $$L = \{x\#y \mid x \neq y, x,y \in \{0,1\}^*\}$$ is a CFL, I could understand $$L = L_1 \cup L_2$$, $$L_1 = \{x\#y\mid|x| \neq |y|\}$$, $$L_2 = \{x\#y \mid|x| = |y|,x \neq y\}$$, and make a CFG for $$L_1$$, but I don't know how to make a CFG for $$L_2$$, since $$y$$ is not a reverse string of $$x$$. How can I know the $$i_\text{th}$$ symbol is different?

Note this question is different from Show that { xy ∣ |x| = |y|, x ≠ y } is context-free since we have an additional separator $$\#$$.