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By Chris Page
BBC News Ireland Correspondent
Rishi Sunak and Liz Truss are due to meet members of the Conservative Party in Northern Ireland as the Tory leadership hustings roadshow rolls in.
There may be a relatively small number of votes at stake but the challenges the new prime minister will face in this part of the UK are among the most complex and delicate.
The protocol
The fact that Northern Ireland has the UK's only land border presented a Brexit brainteaser for negotiators.
Almost everyone involved in the Brexit process agreed there should not be any checkpoints on the frontier with the Republic of Ireland.
It was thought the open border was a powerful symbol of the peace process and that enforcing controls across the meandering frontier would be impractical.
But the conundrum was: how could checks be avoided when the UK was outside the EU with distinct trading rules and the Republic of Ireland remained inside, continuing to follow European regulations?
The solution - agreed between Boris Johnson's government and Brussels - was the Northern Ireland Protocol.
Essentially, the arrangement has kept Northern Ireland in the EU's single market for goods while the rest of the UK has left.
That means there are no checks on the land border but some goods are inspected when they arrive in Northern Ireland from Great Britain to ensure they comply with EU standards.
Unionist political parties claim the protocol amounts to an economic barrier within the UK and they want the trade border in the Irish Sea to be scrapped.
Kyle Thompson, a unionist from Londonderry, says: "When Northern Ireland is treated differently from everywhere else in the UK, obviously that is a big issue.
"The protocol means laws for Northern Ireland are being set by a foreign power - there's no accountability."
The issue has deep implications for London's relations with Brussels, the new PM's relations with the wider Conservative Party and for the fraught political relations in Northern Ireland.
The power-sharing crisis
Northern Ireland has been without a fully-functioning devolved government since Paul Givan of the Democratic Unionist Party (DUP) resigned as first minister in February.
The DUP argues that the Northern Ireland Protocol was brought in without unionists' consent and that has damaged one of the key principles of power sharing.
In May, Sinn Féin replaced the DUP as the largest party at Stormont in the Assembly election.
Michelle O'Neill is in line to be the first republican first minister but under the power-sharing rules she can only take up the role if the DUP agrees to nominate a deputy.
The DUP has insisted it will only do so if the trade border is scrapped.
The party says it made its position clear prior to the election and would be letting down its voters if it relented.
Critics say it would be a breach of international law.
Rishi Sunak has said he would seek to reopen negotiations with the EU on the protocol but would also keep Ms Truss's bill going through Parliament.
The DUP leader Sir Jeffrey Donaldson has not explicitly endorsed either candidate for the Conservative leadership but he has criticised Mr Sunak's approach.
The other four main parties at Stormont say the DUP is acting irresponsibly in blocking the return of devolved government, particularly at a time when financial pressures on families are significantly increasing.
The pound in your pocket
Some statistics suggest rising inflation may hit Northern Ireland harder than other parts of the UK.
Ulster Bank's chief economist in Belfast, Richard Ramsey, points out that Northern Ireland has lower wages and households spend a greater proportion of their income on energy and food.
"People here are facing a bigger squeeze," he explains.
"Consumer spending accounts for more than two thirds of the economy in Northern Ireland so the cost of living is definitely having an effect."
He says there are "pockets of prosperity", with some thriving sectors such as cybersecurity and pharmaceuticals.
The economic challenges include low productivity, which in Mr Ramsey's view is linked to a lack of business investment and educational underachievement.
He also notes that public spending is higher per person than in England, Scotland or Wales but that is not reflected in the quality of the public services - for example, Northern Ireland has the longest hospital waiting times in the UK.
"We need to be more focused on outcomes, rather than just budgets," he says.
In the short-term, he believes a recession is "inevitable".
He says local economic conditions also mean that Northern Ireland would be more "sensitive" to interventions to help people cope with surging prices, such as the £400 discount to energy bills.
Amie Gallagher leads the Focus Project in the Creggan area of Londonderry, which provides training and support to local women.
She thinks the new prime minister should set price caps.
"They should apply to energy, fuel, childcare - everyday expenses which we see people struggling with more and more," she says.
The past
Another controversial piece of legislation deals with how killings from the conflict in Northern Ireland are investigated.
The Northern Ireland Troubles (Legacy and Reconciliation) Bill would set up a new agency which would gather information on deaths.
Suspects who cooperate with the process would get immunity from prosecution.
The bill would also stop inquests and civil court cases related to the Troubles.
Most victims' groups, and all the Stormont political parties, oppose the bill, saying it takes away the hope of justice from bereaved families.
Army veterans' organisations support the government's approach.
The legislation has passed its Commons stages and will be scrutinised by the House of Lords in the coming months.
It is likely to be challenged in the courts.
The politics of the union
The past few years have seen increased debate and public discussion about the constitutional future of Northern Ireland.
A rise in support for parties who are neutral on that issue has seen unionism lose its overall majority in the Stormont Assembly chamber.
However, the number of people voting for parties who want to maintain Northern Ireland's place in the UK is still greater than those backing parties which favour a united Ireland.
The Good Friday Peace Agreement in 1998 said the UK government should call a referendum on Irish unity if it appeared likely a majority in Northern Ireland would vote for a change.
Boris Johnson consistently ruled out calling a border poll, on the grounds the criteria set out in the Agreement had not been fulfilled.
His successor is very unlikely to take a different position.
Future election results in Northern Ireland during the next few years will indicate whether a referendum may become more likely.