Four Vectors, Two Hidden Relations

Consider four vectors in $\mathbb{R}^4$:

$\mathbf{v}_1 = (1,\,1,\,0,\,1), \quad \mathbf{v}_2 = (2,\,1,\,1,\,0), \quad \mathbf{v}_3 = (3,\,2,\,1,\,1), \quad \mathbf{v}_4 = (1,\,0,\,1,\,-1)$

You can check quickly that no two of them are scalar multiples of one another.

What is the largest number of these four vectors that can be chosen to form a linearly independent set?