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A measurement of the top quark mass using events with one charged lepton, missing transverse energy, and jets in the final state, collected by the D0 detector from pp̅ collisions at √s= 1.96 TeV at the Fermilab Tevatron collider, is presented. A constrained fit is used to fully reconstruct the kinematics of the events. For every event a top quark mass likelihood is calculated taking into account all possible jet assignments and the probability that an event is signal or background. Lifetime-based identification of b jets is employed to enhance the separation between tt̅ signal and background from other physics processes and to improve the assignment of the observed jets to the quarks in the tt̅ hypothesis. We extract a multiplicative jet energy scale (JES) factor in situ, greatly reducing the systematic effect related to the jet energy measurement. In a data sample with an integrated luminosity of 425 pb-1, we observe 230 candidate events, with an estimated background of 123 events, and measure mt= 173.7 ± 4.4(stat+JES) +2.1 -2.0(syst) GeV. This result represents the first application of the ideogram technique to the measurement of the top quark mass in lepton+jets events.