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Acceleration of ions from nanofilms with nonadiabatic linearly polarized laser pulses (i.e. pulses having a sharp front) in the regime of full electron evacuation is considered. At the beginning of acceleration, energy of ions follows a parabolic law with time. Then, the rate of acceleration decreases because the ions charge is compensated with the returning electrons. The analytical theory for this process is developed and compared with the results of the two-dimensional particle-in-cell simulations and a good correspondence is established. As a result, ion beams with the maximal energy on the GeV level can be formed with a 1 PW laser pulse, which is available today.