despair vs run out of steam

despair

verb

To cause to despair.
To be hopeless; to have no hope; to give up all hope or expectation.

noun

That which causes despair.
Loss of hope; utter hopelessness; complete despondency.
That which is despaired of.

run out of steam

verb

To run out of energy or motivation.

How often have the words despair and run out of steam occurred in a corpus of books? (source: Google Ngram Viewer )