Let $\mathrm{A}, \mathrm{B}, \mathrm{C}$ be three sets of complex numbers as defined below $$ \begin{aligned} & A=\{z: \operatorname{Im} z \geq 1\} \\ & B=\{z:|z-2-i|=3\} \\ & C=\{z: \operatorname{Re}((1-i) z)=\sqrt{2}\} \end{aligned} $$ Let z be any point in $\mathrm{A} \cap \mathrm{B} \cap \mathrm{C}$ and let w be any point satisfying $|\mathrm{w}-2-\mathrm{i}|<3$. Then, $|\mathrm{z}|-|\mathrm{w}|+3$ lies between