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Restrict movement to axis but in both directions

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I have some particles that need move along a grid in XZ space and make a turn in a random direction every 50th frame. This all works fine mostly with the help of the Network modifier, but a few particles shoot off at a 45 degree angle which I don't want. The Limit modifier works to restrict them but it only allows for movement in positive or negative direction, but not both directions along these axis. Is there a way to restrict the particles to move only along the X and Z axis but in either direction?

Thanks in advance!

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