Consider the subspace S of $\mathbf{R}^4$ spanned by the vectors: $\mathbf{v}_1 = [1, 1, 1, 1]^T$, $\mathbf{v}_2 = [1, 1, 2, 4]^T$, $\mathbf{v}_3 = [1, 2, -4, -3]^T$. Apply the Gram-Schmidt method starting from $\mathbf{v}_1$, then $\mathbf{v}_2$ and finally $\mathbf{v}_3$ to obtain the orthogonal basis of S: $\mathbf{u}_1 = [1, 1, 1, 1]^T$, $\mathbf{u}_2 = [-1, a, b, c]^T$, $\mathbf{u}_3 = [1, d, e, f]^T$, where a, b, c, d, e and f are all integers (rounded to the nearest ones if necessary). What is mod(|a+b+c+d+e+f|,5), where mod(.) is the modulo operator?