4. Given two sets of points on a plane $M=\{(x, y)|| x$ $\left.+y+1 \mid \geqslant \sqrt{2\left(x^{2}+y^{2}\right)}, x, y \in \mathbf{R}\right\}$, $N=\{(x, y)|| x-a|+| y-1 \mid \leqslant 1, x, y \in$ $\mathbf{R}\}$. If $M \cap N \neq \varnothing$, then the range of values for $a$ is
4. $[1-\sqrt{6}, 3+\sqrt{10}]$