AMO · 2027 · Grades 6-7 · Self-study SET 23 Question 7

The absolute value of $N$, symbolized by $|N|$, represents the distance from the signed number $N$ to the origin, without regard to sign. For example, $|+5|=5$ and $|-3|=3$. Find the sum of the integer values of $N$ that satisfy $2<|N-3|<5$.

**Input:** Enter the integer only, without units.