organic chemistry electron-pushing mechanism?

complete the electron-pushing mechanism for the following ether synthesis from propanol in concentrated sulfuric acid at 140 °C by adding any missing atoms, bonds, charges, nonbonding electron pairs, and curved arrows.

This took me a little while but I finally got it, In the third step you have to add a H to the oxygen that has a single lone pair and also give it a positive formal charge. Then the lone pair from the H2O goes after the H of the electrophilic oxygen and becomes H3O+. The electron pair connecting the H to the electrophilic O becomes a lone pair of the O.

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