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.
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