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The first time they met in Budapest, they started on opposite sides of a complex operation, ended up saving each other's lives in a mutual bid for survival, and holed up afterward in a safehouse, sharing vodka and stories until she told him to call her Natasha and didn't retract when Clint mentioned that was a name between friends.
The second time they met, Clint dragged her out of a burning hospital (she'd lit the match, she was guilty, and her ledger dripped) and held her on a safehouse floor as she wept for the dead children and her own memory of a burning building before the Red Room came to take her away.
The third time, Natasha saw him lower his bow and hold out his hand with a simple request to come with him, stay with him because they made each other whole (and he loved her but he didn't say it, and she loved him and she did).