Did Jesus Die Before Or After Passover?

Skeptics and critics of the Bible often claim that the gospel of John contradicts the gospels of Matthew, Mark, Luke and John, in reporting Jesus died before, rather than after, the Passover. Did Jesus die before, or after, Passover?
Alleged contradiction:
Was Jesus crucified on the daytime before the Passover meal or the daytime after?
(a) After (Mark 14:12-17)
(b) Before. Before the feast of the Passover (John 13:1) Judas went out at night (John 13:30). The other
disciples thought he was going out to buy supplies to prepare for the Passover meal (John 13:29). When
Jesus was arrested, the Jews did not enter Pilate’s judgment hall because they wanted to stay clean to
eat the Passover (John 18:28). When the judgment was pronounced against Jesus, it was about the sixth
hour on the day of Preparation for the Passover (John 19:14)