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“Shape of You,” the No. 1 song of 2017, could have ended up an album track by Rihanna or U.K. girl group Little Mix. Its eyebrow-raising, sense-stimulating line about the scent of bedsheets came close to being, “My T-shirt smells like you.” It certainly wasn’t meant for an Ed Sheeran album when the singer, along with co-writers and producers Steve Mac and Johnny McDaid, gathered in a London studio last winter. By that time, “÷” (“Divide”), Sheeran’s third release, which has moved 900,000 project units to date, was ostensibly done and ready to be turned in. The three were giving collaboration a no-pressure go to see what they’d come up with. The result after just two hours: a hit that’s the biggest of each of their respective careers.

Mac, who’s written a dizzying 23 chart-toppers in his native Britain, says it all started with an off-the-cuff pizzicato progression on his Mellotron keyboard. “It was very first thing I played,” he says. “Certain sounds trigger certain melodies, vibes or styles. Ed just started to flow with a verse — that sung-rap thing that nobody else does like Ed Sheeran – and, while I’d love to say it took hours, he works so fast that by hour two, we were putting down vocals.”

McDaid, a member of the rock band Snow Patrol whose songwriting credits include Pink’s current hit “What About Us,” laughs remembering how Mac, whom he hadn’t met before, mistook him as “Ed’s assistant.” Then again, he’s accustomed to such situations. “It’s like some sort of odd speed dating: ‘Hi. Nice to meet you. Tell me everything about yourself and do it really well and quickly.’”

It turned out to be a match that created a smash. “Steve is a master craftsman,” says McDaid. “His focus is on the end result or the destination, and my mind is in the moment a lot of the time.” It helped, adds Sheeran’s longtime co-writer, “that in Ed’s mind it wasn’t a song for him. It was a character, a playful diary of a vignette.”

Still, there were forks in the road and crucial structural decisions to be made — that racy “Now my bedsheets smell like you” lyric, for starters. Says McCaid: “I fought it. It’s such a bold line because the inference is that there’s sex, and the smell of something very intimate. I wanted it to be T-shirt because it felt more playful.” Sheeran’s response? “Ed said, ‘No, it’s f—king bedsheets,’” McDaid laughs. “And what that did is really take the guessing out of it. Ed – f—cking genius. I almost ruined it.”

Other considerations arose about using “I’m in love with your body” in the chorus – did it objectify women? McDaid’s take: emphasize “shape of you” and the sentiment behind it by using it as the title. “It’s an Irish expression that has a different meaning for me,” he says. “Shape is figurative, not necessarily physical. The shape of someone is everything — it’s the way they appear in the world, it’s the essence of them.”

After some basic percussion was added (courtesy of Sheeran’s trademark hand-work on the body of his guitar), the singer took the unfinished rough to a meeting later that day with Atlantic Records UK chief Ben Cook and A&R executive Ed Howard. Cook, who presciently signed the acoustic guitar- and loop pedal-wielding kid few would have pegged to be the biggest white male pop star on the planet, and Howard were the ones to first suggest a Sheeran-Mac-McDaid session.

“They’re quite exceptional as A&R men because they don’t listen to music as a commodity in the moment, they figure out how to make it happen on a commercial level later,” says McDaid. “In that room that day Stuart [Camp], Ed’s manager, Ben and Ed all looked at us and said, ‘That’s a f—ing hit.’ And [today], it’s pretty much the same song.”

“It was one of the eureka moments of my life,” Cook concurs. “The moment we it heard I we knew we’d found something that was very special. We’d heard amazing songs, like ‘Save Myself’ and ‘How Do You Feel’, ‘Eraser.’ But when I asked Ed how it had gone with Steve Mac he said he’d written something, but it wasn’t for him. Right at the end of the night when I had to leave, I asked him again if we could hear the song… He put it on Steve’s demo, and literally in the moment I turned to him and said ‘this is a f—ing smash!’”

“It’s special because it’s extremely simple,” Howard adds. “It’s built from a small number of very potent musical elements: Sheeran vocal stylings, idiosyncratic lyrics, organic percussion and of course acoustic guitar, but reframes them in a progressive and fresh way.”

Finished album be damned, Cook and Howard made the executive decision to have it mixed (by Mike “Spike” Stent over 10 days), add it onto the track list and launch it concurrently with the wistful “Castle on the Hill.”

“I thought ‘Shape of You’ would program really well,” says Mac. “Still it’s a brave move in that it can be a logistical nightmare for record companies or radio stations to have two singles to choose from. But the album is called ‘Divide.’”

As it turned out, they played both. “Castle on the Hill,” with 1.9 million project units, is No. 34 for the year. “Shape of You” clocks in at 5.5 million with 2.5 million in pure song sales (downloads). In the U.K., only “Bohemian Rhapsody” and “Candle In the Wind 1997” have sold more.