In a singly ionised helium ion ($\text{He}^+$, $Z = 2$), the electron jumps from the level $n = 6$ to the level $n = 4$ and emits a photon. A hydrogen atom emits a photon of exactly the same wavelength when its electron jumps to the level $n = 2$ from a higher level $n$. The value of this higher level $n$ is ____.