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```import java.util.*;

public class MinimumConnectedSets {

public static void main(String[] args) {
List<Integer> a = Arrays.asList(3, 2, 3);
List<Integer> b = Arrays.asList(5,9,3);
int k = 10;

int result = minimumDivision(a, b, k);
System.out.println("Minimum connected sets: " + result); // Expected output: 2
}

public static int minimumDivision(List<Integer> a, List<Integer> b, int k) {
int n = a.size();
List<int[]> intervals = new ArrayList<>();

// Combine a and b into intervals
for (int i = 0; i < n; i++) {
}

// Sort intervals by the start value
intervals.sort(Comparator.comparingInt(interval -> interval[0]));

int originalConnectedSets = countConnectedSets(intervals);
int minConnectedSets = originalConnectedSets;

// Try inserting the segment between every possible pair of intervals
for (int i = 0; i <= n; i++) {
int[] newInterval;

if (i == 0) {
// Insert segment before the first interval
newInterval = new int[]{intervals.get(0)[0] - k, intervals.get(0)[0]};
} else if (i == n) {
// Insert segment after the last interval
newInterval = new int[]{intervals.get(n - 1)[1], intervals.get(n - 1)[1] + k};
} else {
// Insert segment between intervals[i-1] and intervals[i]
int start = intervals.get(i - 1)[1];
int end = intervals.get(i)[0];
newInterval = new int[]{start, start + k};

// Ensure that the new interval does not overlap the next one
if (newInterval[1] > end) {
newInterval[1] = end;
}
}

// Simulate inserting the new interval
List<int[]> newIntervals = new ArrayList<>(intervals);
newIntervals.sort(Comparator.comparingInt(interval -> interval[0]));

// Count the connected sets with the new interval inserted
int connectedSets = countConnectedSets(newIntervals);
minConnectedSets = Math.min(minConnectedSets, connectedSets);
}

return minConnectedSets;
}

private static int countConnectedSets(List<int[]> intervals) {
int connectedSets = 1;
int currentEnd = intervals.get(0)[1];

for (int i = 1; i < intervals.size(); i++) {
int[] current = intervals.get(i);
if (current[0] > currentEnd) {
connectedSets++;
currentEnd = current[1];
} else {
currentEnd = Math.max(currentEnd, current[1]);
}
}

return connectedSets;
}
}
```