Naturally Dyed Deviled Easter Eggs

6 large eggs

1 cup blackberries (fresh or frozen)

1 cup blueberries (fresh or frozen)

1 tbs ground turmeric

1 cup grape juice

1 cup pickled beet juice

4 tsp vinegar, divided

Filling

1/3 cup of mayonnaise 

1 ½ tsp yellow mustard

1/8 tsp salt