encourage vs keep at arm's length

encourage

verb
  • To mentally support; to motivate, give courage, hope or spirit. 

  • To spur on, strongly recommend. 

  • To foster, give help or patronage 

keep at arm's length

verb
  • Avoid a close relationship. 

  • Avoid direct confrontation or struggle. 

  • Keep at a distance, away from one's body. 

How often have the words encourage and keep at arm's length occurred in a corpus of books? (source: Google Ngram Viewer )