Why did the Allied Forces believe capturing Rome was important?

The italian campaign of world war II was the name of allied operations in and around italy, from 1943 to the end of the war in europe

They believed capturing Rome would lead Italy to remove itself from World War II.

They believed capturing Rome would draw German troops away from the Soviet front.

They believed capturing Rome would allow for an invasion of France.

They believed capturing Rome would signal the end of German dominance in Europe.