Is the dust stirred up while walking, which contains donkey dung, considered ritually impure if it enters one's shoe and touches the sole of the foot?

The dust that sticks to the feet while walking does not cause harm and does not require washing, because dry met dry and thus does not render it impure. Even if the foot were wet, it would not be rendered impure because it is pardoned due to its frequent occurrence. Even if it were a lot, it would not render it impure because the original state is purity. However, it is preferable to wash the feet as a precaution and for cleanliness.