1. Find all possible integer values of the expression $\frac{2}{a}+5+\sqrt{2}$, given that $a-\sqrt{2}$ is also an integer. Write the answers in any order, separated by commas or semicolons.

Example of answer format: $1 ; 2$
Answer: $3,7\|7,3\| 3 ; 7 \| 7: 3$