How do we perform the isomerisation of 1-butyne to 2-butyne using NaNH2?

How do we perform the isomerisation of 1-butyne to 2-butyne using NaNH2? As a first step, I think that $\ce{NH2^-}$ would remove $\ce{H^+}$ from the third carbon to give an allene intermediate. But I don't know how to proceed after that. Please explain the other steps.




Here in the following image I have explained the mechanism for transformation of 2-alkyne to 3-alkyne. Isomerisation from 1-butyne/ 1-alkyne to 2-butyne / 2-alkyne is not possible.


[![Mechanism](https://i.stack.imgur.com/hFz3O.jpg)](https://i.stack.imgur.com/hFz3O.jpg)


Hope it helps.


 -1