USA and Africa have 4 forms of frontiers!

For 2 totally different USA states the 4 prospects occur contemplating their frontiers:

• They do not share any frontier (e.g. Alaska and Utah or Florida and California)
• They share a straight frontier (Montana and South Dakota)
• They share a fractal frontier and a straight frontier (Texas and Oklahoma)
• They share a fractal frontier (Tennesse and North Carolina)

The identical happens for African international locations:

• They do not share any frontier (e.g. Madagascar and Egypt)
• They share a straight frontier (Western Sahara and Morocco)
• They share a fractal frontier and a straight frontier (Egypt and Lybia)
• They share a fractal frontier (Ethiopia and Sudan)

Swap as many US states and African international locations such that the variety of neighbors do not change and the kind of frontier additionally doesn’t change! As soon as a state or a rustic has been swapped, it cannot be swapped once more.

As a trivial begin, Alaska will be swapped with Madagascar as they do not share any frontier with every other state or nation.

Then, Florida has two neighbors, Alabama and Georgia and Florida shares solely fractal frontiers with each of them. The identical happens for Tunisia which has two neighbors, Algeria and Lybia and Tunisia shares solely fractal frontiers with each of them. Consequently, Florida and Tunisia may very well be swapped.

You cannot swap Washington with Morocco even when they’ve the identical variety of neighbors (Idaho and Oregon for Washington) and (Western Sahara and Algeria for Morocco) as a result of Washington shares fractal frontiers with Oregon and fractal and straight frontiers with Idaho whereas Morocco shares straight frontiers with Western Sahara!

What number of pair State(USA)-Nation(Africa) will be swapped at most?

Please think about the next two lists for this puzzle:

1. Alabama
2. Alaska
3. Arizona
4. Arkansas
5. California
6. Colorado
7. Connecticut
8. Delaware
9. Florida
10. Georgia
11. Hawaii
12. Idaho
13. Illinois
14. Indiana
15. Iowa
16. Kansas
17. Kentucky
18. Louisiana
19. Maine
20. Maryland
21. Massachusetts
22. Michigan
23. Minnesota
24. Mississippi
25. Missouri
26. Montana
27. Nebraska
28. Nevada
29. New Hampshire
30. New Jersey
31. New Mexico
32. New York
33. North Carolina
34. North Dakota
35. Ohio
36. Oklahoma
37. Oregon
38. Pennsylvania
39. Rhode Island
40. South Carolina
41. South Dakota
42. Tennessee
43. Texas
44. Utah
45. Vermont
46. Virginia
47. Washington
48. West Virginia
49. Wisconsin
50. Wyoming

And:

1. Algeria
2. Angola
3. Benin
4. Botswana
5. Burkina Faso
6. Burundi
7. Cabo Verde (Cape Verde)
8. Cameroon
9. Central African Republic
10. Chad
11. Comoros
12. Republic of the Congo
13. Democratic Republic of the Congo
14. Côte d’Ivoire (Ivory Coast)
15. Djibouti
16. Egypt
17. Equatorial Guinea
18. Eritrea
19. Eswatini (previously Swaziland)
20. Ethiopia
21. Gabon
22. The Gambia
23. Ghana
24. Guinea
25. Guinea-Bissau
26. Kenya
27. Lesotho
28. Liberia
29. Libya
30. Madagascar
31. Malawi
32. Mali
33. Mauritania
34. Mauritius
35. Morocco
36. Mozambique
37. Namibia
38. Niger
39. Nigeria
40. Rwanda
41. São Tomé and Príncipe
42. Senegal
43. Seychelles
44. Sierra Leone
45. Somalia
46. South Africa
47. South Sudan
48. Sudan
49. Tanzania
50. Togo
51. Tunisia
52. Uganda
53. Zambia
54. Zimbabwe