Consider a real sequence x[n] that has all the poles and zeros of its z-transform inside the unit circle. Determine, in terms of x[n], a real sequence x₁[n] not equal to x[n], but for which x₁[0] = x[0], |x₁[n]| = |x[n]|, and the z-transform of x₁[n] has all its poles and zeros inside the unit circle.