Persian Presidents: "Capture a Hero that was or is set aside..."
Samaritan Water Jar: "Discard this card to reveal the top 3 cards of an opponent's deck... and set them aside... When that deck has no cards, return those cards from set-aside to deck."
If Samaritan Water Jar sets aside a Hero and then that Hero returns to the deck and enters play, can Persian Presidents capture it? Or is "was previously set-aside" something that resets upon going into the deck?