Beijing: At first glance, it seems the perfect solution to the world's most dangerous standoff: Find a way to get China to use its enormous influence to force North Korea to abandon its nuclear bombs.
The countries, after all, share a long, porous border, several millennia of history and deep ideological roots. Tens, and possibly hundreds, of thousands of Chinese soldiers, including Mao Zedong's son, died to save North Korea from obliteration during the Korean War, and China is essentially Pyongyang's economic lifeline, responsible for most of its trade and oil.
The notion of Chinese power over the North — that the countries are as "close as lips and teeth," according to a cliche recorded in the 3rd century — is so tantalising that Donald Trump has spent a good part of his young presidency playing it up.
The reality, however, is that the complicated, often exasperating, relationship is less about friendship or political bonds than a deep and mutually uneasy dependency. Nominally allies, the neighbors operate in a near constant state of tension, a mix of ancient distrust and dislike and the grating knowledge that they are inextricably tangled up with each other, however much they might chafe against it.
This matters because if China is not the solution to the nuclear crisis, then outsiders long sold on the idea must recalibrate their efforts as the North approaches a viable arsenal of nuclear-tipped missiles capable of reaching the US mainland, something the CIA chief this week estimated as only a matter of months away.
"The North Koreans have always driven China crazy," says John Delury, an expert on both countries at Seoul's Yonsei University, "and, for their part, the North Koreans have always felt betrayed by China. But both sides need each other in elemental ways."
THE VIEW FROM CHINA: "KIM FATTY"
One clue about how Chinese see the North can be seen in two widespread nicknames for the overweight, third-generation North Korean leader, Kim Jong Un: Kim Fatty The Third and Kim Fat Fat Fat.
As China rises as an economic, military and diplomatic heavyweight whose reach extends from the Americas to Asia, many here resent being dragged down by an impoverished, stubborn, Third World dictatorship that allows its people to go hungry while its leader lives in luxury and expands a nuclear arsenal that could lead to war with Washington.
North Korean missile tests hurt trade and tourism and strengthen the US presence in a region that China believes it should dominate. North Korean nuclear tests set off earthquakes near the Chinese border and raise fears of radioactive contamination.
There's also scorn for the North's brutal, nepotistic brand of socialism, and displeasure that North Korean aggression led South Korea to allow on its territory a US anti-missile system that Beijing says can be used to spy on its operations.
This growing disdain is reflected in China's willingness to permit criticism of the North in the press, and to allow tougher sanctions at the U.N. Beijing has suspended coal, iron ore, seafood and textiles from the North.
Although North Korea takes pride in its ability to absorb pain, be it war, famine, sanctions or condemnation, China's tougher line will rob Pyongyang of key sources of foreign currency.
Still, nothing China has done offsets its underlying fear that too much external pressure could collapse the government in Pyongyang. The nightmare scenario for Beijing is North Korean refugees flooding into its northeast after Seoul takes power in Pyongyang and US and South Korean troops occupy lands that were once considered a buffer zone.
"It is true that China loathes North Korea and vice versa — at the societal level, the leadership level and the governmental level," Van Jackson, a North Korea specialist and lecturer at Victoria University of Wellington in New Zealand, wrote earlier this year. "But China's 'emotions' toward North Korea don't drive its policy."
Beijing has also argued that it has less power over North Korea than people think. Some observers question whether China could force a change in the North, short of military intervention, even if it wanted to.
North Korea relies on China for most of its oil, and outsiders have long argued that the best way to cripple the North's economy and force it to submit would be to persuade Beijing to cut that flow.
But even this may not work.
North Korea gets its oil from China out of convenience, not necessity, according to Pierre Noel, an energy security specialist at the International Institute for Strategic Studies think tank.
"Would it be good news for North Korea if the oil stopped flowing? No. Is it likely to cripple the economy and force the government to change course on their foremost strategic priority? No. There are ample hydrocarbons in North Korea to substitute for those it imports from China."
THE VIEW FROM NORTH KOREA: "PROFOUND MISTRUST"
One way to gauge Pyongyang's feelings for Beijing is to consider that Kim Jong Un has yet to visit his only major ally, a country that accounts for 90 percent of North Korean trade, since taking power in December 2011.
His late father, Kim Jong Il, hated to travel but went to China eight times during his rule, and Chinese leaders reciprocated with trips to Pyongyang.
Since communication at the highest levels has now virtually disappeared, Kim Jong Un feels little need to pay attention when Beijing calls on him to stop testing nukes and missiles.
In fact, North Korea has seemingly sought to humiliate Beijing by timing some of its missile tests for major global summits in China.
Last month, North Korean state media accused Chinese state-controlled media of "going under the armpit of the US" by criticising Pyongyang. In May, the North vowed to "never beg for the maintenance of friendship with China (or risk North Korea's) nuclear program which is as precious as its own life, no matter how valuable the friendship is."
It can be argued that the North Korea-China relationship never really recovered from Beijing's decision in 1992 to establish formal diplomatic relations with Seoul.
But a big part of North Korea's "profound sense of mistrust" and "long-term effort to resist China's influence" stems from the 1950-53 Korean War, according to James Person, a Korea expert at the Wilson Center think tank in Washington. The war is often seen as the backbone of the countries' alliance, he said, but the North blamed the failure to conquer the South on Beijing, which had seized control of field operations after the near-annihilation of North Korean forces.
In the 1970s, with North Korea pushing the United States for a peace treaty to replace the Korean War cease-fire that continues today, Washington chose to work through China.
By so doing, US officials failed to see the limits of Chinese influence in the North, Person wrote last month on the 38 North website.
"Yet, nearly four decades later, asking China to solve the North Korean problem remains Washington's default policy for dealing with Pyongyang." This, he said, is "a recipe for continued failure."