CLT constants for scaled discrete variables

Let $X_1, X_2, \dots$ be a sequence of independent random variables such that $$P(X_i = i) = \frac{1}{4}\quad\text{and}\quad P(X_i = 2i) = \frac{3}{4},\quad i=1, 2, \dots.$$ For some real constants $c_1$ and $c_2$, suppose that $$\frac{c_1}{\sqrt{n}}\sum_{i=1}^n \frac{X_i}{i} + c_2\sqrt{n} \xrightarrow{d} Z \sim N(0, 1),\quad\text{as }n\to\infty.$$ Then, the value of $\sqrt{3}(3c_1+c_2)$ equals