Construction of separately continuous functions of $n$ variables with given restriction

It is solved the problem on construction of separately continuous functions on product of $n$ topological spaces with given restriction. In particular, it is shown that for every topological space $X$ and $n-1$ Baire class function $g:X\to \mathbb{R}$ there exists a separately continuous function $f:X^n\to \mathbb{R}$ such that $f(x,x,\dots ,x)=g(x)$ for every $x\in X$.