water in a saucepan. Heat until water comes to a full boil. Remove from heat and let stand in water for 20 minutes. Run cold water over eggs to cool them quickly. Peel eggs. Mix brown sugar, granulate sugar, salt, water and vinegar and heat until sugar is dissolved, stirring occasionally. Add red beets and juice to this mixture and pour over the pee eggs. Refrigerate at least 12 hours. Serve eggs sliced in half.