Non-negative integers $d_i$, $i\in \mathbb Z$, satisfy the following condition: $$d_k=|\{i<k: d_i+i\geq k\}|$$ for every integer $k$. Prove that there is a positive integer $n$ such that $$d_k\in \{n-1,n\}\ \ \text{and}\ \ d_{k+n}=d_k$$ for every integer $k$.