Why did Littlefinger let Sansa marry Ramsay?

Why did Littlefinger let Sansa marry Ramsay? On the surface, Littlefinger gets to appear (at least to the Boltons) as if he’s helping the Boltons secure the North, since the Northern lords preferred to have a Stark in Winterfell. But he told Sansa the marriage could help her avenge her family, by destroying the Boltons from within.

On the surface, Littlefinger gets to appear (at least to the Boltons) as if he’s helping the Boltons secure the North, since the Northern lords preferred to have a Stark in Winterfell. But he told Sansa the marriage could help her avenge her family, by destroying the Boltons from within.