A liquid $\boldsymbol{L}$ containing a dissolved gas $\boldsymbol{S}$ is stripped in a countercurrent operation using a pure carrier gas $\boldsymbol{V}$. The liquid phase inlet and outlet mole fractions of $\boldsymbol{S}$ are $0.1$ and $0.01,$ respectively. The equilibrium distribution of $\textbf{S}$ between $\textbf{V}$ and $\boldsymbol{L}$ is governed by $\boldsymbol{y}_{\boldsymbol{e}}=\boldsymbol{x}_{\boldsymbol{e}}$, where $\boldsymbol{y}_{\boldsymbol{e}}$ and $\boldsymbol{x}_{\boldsymbol{e}}$ are the mole fractions of $\boldsymbol{S}$ in $\boldsymbol{V}$ and $\boldsymbol{L}$, respectively. The molar feed rate of the carrier gas stream is twice as that of the liquid stream. Under dilute solution conditions, the minimum number of ideal stages required is__________(in integer).