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For South Koreans living next door to a hostile, nuclear-armed state that regularly threatens their annihilation, their vote in Tuesday's presidential election likely will be based in part on each candidate's plan for how to handle North Korea.

The North Korea conundrum is a perpetual foreign policy headache for South Korea's leaders and one that is impacting the presidential race in several ways:

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THE CHOICES

The current front-runner is liberal candidate Moon Jae-in, a former human rights lawyer who has repeatedly called former President Park Geun-hye's North Korea policy a complete failure. He wants to improve ties with Pyongyang by abandoning the hard-line approach to the North favored over the past decade by conservative governments.

His chief rival is former software mogul Ahn Cheol-soo, who is more centrist than Moon and has a tougher stance on North Korea that would more closely align with the conservative approach of sanctions, pressure and promises of aid in return for disarmament.

Many traditional conservatives still reeling from Park's downfall and her arrest support Ahn because they worry Moon's ascension would lead to concessions to the North and weaken international sanctions on the country.

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SUNSHINE OR SHADE

The debate over how to deal with North Korea has intensified as Pyongyang has grown bolder with its nuclear and missile tests and other provocations, such as 2010 attacks that killed 50 South Koreans.

Moon has argued that conservative incompetence is to blame for North Korea's actions. He says he'd use both pressure and dialogue to deal with Pyongyang and try to promote cross-border economic integration.

Moon was chief of staff for late liberal President Roh Moo-hyun, who continued the "sunshine" policy of engaging with the North started by his predecessor President Kim Dae-jung. During his 2003-2008 term, Roh pushed to ease animosity with cross-border projects and by shipping food and other aid to the North with little or no strings attached.

Conservatives portray Moon as a Pyongyang sympathizer. They say past liberal governments gave aid despite suspicions that much of it went to North Korea's military instead of its hungry citizens. They contend that the inter-Korean projects yielded few results.

Ahn talks about bolstering the armed forces and strengthening the military alliance with the United States, an apparent effort to rally conservative support. But most of his party members are dissenters from Moon's main opposition Democratic Party. That has raised questions about how Ahn would actually manage North Korea affairs if elected.

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THE TRUMP CARD

Many see a Moon presidency as hurting ties with the U.S., Seoul's most important ally, and setting up a potential clash with President Donald Trump, whose administration recently settled on a strategy that emphasizes increased pressure on Pyongyang with the help of China, the North's main aid benefactor.

Moon has said repeatedly that he won't tolerate any provocation by North Korea and has vowed to boost surveillance and anti-missile capabilities. He also says he wants a more assertive South Korea, which would persuade Washington to improve ties with Pyongyang, try to restart dormant regional disarmament-for-aid talks and push for a permanent peace treaty on the Korean Peninsula.

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KIM JONG UN

Times have changed since liberals were last in charge in Seoul and many experts don't expect that Moon would push for any big reconciliation projects because North Korea has gone too far in its nuclear development over the last decade.

Public views on North Korea have also changed a lot since Kim Jong Un became leader in 2011 and began cementing his power by executing officials, upping the number of missile launches and conducting three nuclear tests. Fewer South Koreans still believe economic assistance could get the North to abandon its nuclear ambitions.

Still many analysts believe that both Moon and Ahn would at least open the door for talks with North Korea.

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MISSILE DEFENSE

Also at play is Park's decision to allow the deployment of a sophisticated U.S. missile-defense system to cope with the North Korean threat. China, South Korea's largest trading partner, sees the system's radars as a threat to its own security and has retaliated by such measures as halting package tours to the South.

Moon is critical of the Terminal High-Altitude Area Defense system deployment, or THAAD. Ahn initially opposed THAAD deployment but later supported it amid deepening anti-North Korea sentiments. Moon also toned down his THAAD criticism, saying its deployment would be inevitable if North Korea continued provocations.