demented vs few cards shy of a full deck

demented

adj
  • Insane or mentally ill. 

  • a demented idea 

  • Crazy; ridiculous. 

  • Suffering from dementia. 

few cards shy of a full deck

adj
  • mentally deranged; demented; insane. 

How often have the words demented and few cards shy of a full deck occurred in a corpus of books? (source: Google Ngram Viewer )