Remove short length pulses

It is required to eliminate short length pulses from a sampled data. It means 0’s in continuous 1’s have to be made 1 & similarly 1’s in 0’s are to made 0’s as shown in the following example. Give the FSM for the same.

Eg: I/P 0 1 0 0 1 1 0 1 1 0 0

O/P 0 0 0 0 0 1 1 1 1 1 0