N identical uncharged capacitors are connected in series with a battery and a switch. The switch is closed and kept closed until the capacitors are completely charged. Let the total potential energy stored now in all the capacitors be ${\text{U}}_{\text{1}}$. Now, the switch is opened, the battery is removed from the circuit and an identical uncharged capacitor is connected in its place. Now the switch is closed again and kept closed for a long time. The total potential energy stored in all the capacitors is now ${\text{U}}_{\text{F}}$. If $\frac{{\text{U}}_{\text{F}}}{{\text{U}}_{\text{I}}}\text{=}\frac{\text{1}}{\text{6}}\text{,}$ then N is __________.