First the FFT of $$x[n]=[1, 1, 1, 1]$$ and its inverse for $N=2^3$

[![enter image description here][1]][1]

where red dot indicates sample location.

Now shift samples as given by you,

[![enter image description here][2]][2]

I may be totally wrong but keen to learn my mistakes
  [1]: https://i.sstatic.net/4TaW3.png
  [2]: https://i.sstatic.net/WuxAE.png