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Octupole instabilities in even-even nuclei near nucleus have been investigated by means of improved total-Routhian-surface calculations with the inclusion of reflection-asymmetric deformations. It is found that the shape evolutions of mirror nuclei are similar between Z = 56 isotopes and N = 56 isotones in the ground-states. As an example, , which has reflection-symmetric shape at low spins, is predicted to be octupole deformed at certain high rotational frequencies. The prediction is confirmed by experiment.