A network security administrator partitions a network of $N = 1000$ servers into three security zones, $Z_1, Z_2, Z_3$, such that every server is placed in at least one zone. Due to configuration overlaps, some servers are in multiple zones:

• $|Z_1| = 600$, $|Z_2| = 500$, $|Z_3| = 400$.
• The number of servers in both $Z_1$ and $Z_2$ is twice the number of servers in all three zones.
• The number of servers in both $Z_2$ and $Z_3$ is $1.5$ times the number of servers in all three zones.
• The number of servers in both $Z_1$ and $Z_3$ is $2.5$ times the number of servers in all three zones. Determine the number of servers that belong to exactly one security zone.