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]:. Nevertheless, the https://i.sstatic.net/WuxAE.png$\left|x[n]\right|$