#Pyth, <s>36</s> 32 bytes

    }QsM^+ks._Mc6"logsincostanlnee"l

[Try it online.][try]

Extremely inefficient.

[try]: https://pyth.herokuapp.com/?code=%7DQsM%5E%2Bks._Mc6%22logsincostanlnee%22l&input=%22clogs%22&debug=0