Kim Kardashian, Kanye West

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UPDATE: Kim Kardashian, Kanye West and baby North West have left the building! E! News has exclusively confirmed that the happy trio left Cedars-Sinai hospital overnight, just shy of a week after the new mom checked in and gave birth (a full five weeks earlier than expected!). The new family unit is heading to an undisclosed home in Los Angeles.

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Finally, Baby Kimye has a name!

E! News has confirmed that Kim Kardashian and Kanye West's little daughter is named...

North West

Forget One Direction, this little girl goes 'em one better with two directions.

A source close to the couple confirms to E! News that the girl's name is North West, with no middle name.

According to a source, "They will call her Nori for short!"

"She has black straight hair! Lots of it! Looks like a good mix of both of them [Kanye and Kim] but more like Kim," says the source. "She's adorable!"

"Kanye is so in love with her. He won't leave her side."

It's been an action-packed week for the new family, with the baby arriving 5 weeks early on Saturday June 15, 2013, at Cedars-Sinai hospital in Los Angeles.

Kongrats to Nori and her proud parents!

(Originally published on June 20, 2013 at 9:06 p.m. PT)

Tune in to Keeping Up with the Kardashians on Sundays at 9 p.m., only on E!

PHOTOS: Take a look back at Kim Kardashian and Kanye West's road to baby!

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