cut in vs put one's two cents in

cut in

verb
  • To begin riding a wave in front of someone else whose legitimate turn it is. 

  • To join a queue in the middle, as opposed to at the back. 

  • To pull in front of another vehicle in traffic, especially to do so dangerously or unfairly. 

  • When painting, to paint edges, corners, or trim in preparation for rolling larger areas. 

put one's two cents in

How often have the words cut in and put one's two cents in occurred in a corpus of books? (source: Google Ngram Viewer )