Maximize Sugar Cubes

An ant climbing down an ant-hill can choose to go either down and to the right or down and to the left at each level until it reaches the bottom of the hill. And at each junction, the ant collects a number of sugar grains indicated by the numbers in the circle.

Being greedy, this ant believes that if it always moves down towards the larger of the two values directly below, it will be able to collect the largest number of sugar grains overall. With the hill as shown above, is this greedy strategy optimal for collecting sugar?

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