$$\mathbf{X}^{a+}$$ and $$\mathbf{Y}^{b+}$$ are hydrogen-like species. The wavelength of light absorbed during the transition between the states with principal quantum numbers $$n=1$$ and $$n=2$$ of $$\mathbf{X}^{a+}$$ is $$\lambda$$. The wavelength of light absorbed during the transition between the states with principal quantum numbers $$n=2$$ and $$n=4$$ of $$\mathbf{Y}^{b+}$$ is $$9\lambda$$. The lowest possible value of $$(a+b)$$ is ___.