head for the hills vs run a mile

head for the hills

verb
  • To go to a safe place; to seek refuge; to flee. 

  • To travel to a higher elevation, especially to a rural region on vacation. 

run a mile

verb
  • To escape, flee or leave a situation or relationship, usually as a result of a shocking or sudden announcement or revelation. 

How often have the words head for the hills and run a mile occurred in a corpus of books? (source: Google Ngram Viewer )