My solution:

    0: Z 2
    1: Z 3
    2: J 0 2 -> 4
    3: J 1 3 -> 7
    4: I 2
    5: J 0 2 -> 4
    6: J 1 3 -> 7
    7: I 2
    8: I 3
    9: J 1 3 -> 7

Handles the zero case. Only uses 4 cells total.