Consider solving the following system by Jacobi iteration scheme

$$\begin{array}{l}x+2 m y-2 m z&=1 \\ n x+y+n z&=2 \\ 2 m x+2 m y+z&=1 \end{array}$$

where $m, n \in \mathbb{Z}$. With any initial vector, the scheme converges provided $m, n$, satisfy

1. $m+n=3$

2. $m>n$

3. $m<n$

4. $m=n$