Patrick causes an accident while driving his car. The driver of the other car is injured and is awarded damages of $$750,000.$ Patrick has an auto policy liability limit of $$300,000.$ However, it is later discovered that the amount due from Patrick's auto insurer is uncollectible. Patrick also has an umbrella policy with a $$1,000,000$ limit of liability. What amount will the umbrella insurer pay for this accident?

$$749,000$

$$450,000$

$$750,000$

$$449,000$