#soft-thresholding

The features are orthonormal ($X^\top X = I$) and the OLS coefficients are $\hat\beta = (3,\ 0.5,\ -1.2,\ 0.8)$. You fit the lasso, minimizing $\tfrac12\lVert \mathbf{y} - X\boldsymbol\beta\rVert^2 + \lambda\lVert\boldsymbol\beta\rVert_1$ with $\lambda = 1$. How many of the four lasso coefficients are exactly zero?