Follow the red marks on the Hand Drawn Map

This quest is obtained after picking up the Hand Drawn Map thrown into the well.

Quest Description
There's some red marks drawn on this map. I wonder if it can help me to escape from here...
 * Climb up the Well
 * Find a Water Source
 * Find the Coastal Tower
 * Go down the Tower
 * Follow the Shore Path
 * Cross the Gate
 * Reach the High Tower