Test case 5 seems to be incorrect.

6
-5 15 25 71 63

There are only 5 numbers provided, not 6. Anyone else getting this? I seem to get full points without it though.

sort and then check the diff of two adjecent numbers.. keep tracking the min value, update the both pairs in a list, if the new pair is having less than last min value, then delete the list, update with new pairs,, if the new pair is having exact value, add them in list too.

n =  input()
nums = list(map(int,input().strip().split()))
nums.sort()
lowestDiff = nums[1]-nums[0]
res = [nums[0],nums[1]]
for i in range(1,len(nums)-1):            
    if nums[i+1]-nums[i] < lowestDiff:
        res = []   
        res.append(nums[i])
        res.append(nums[i+1])
        lowestDiff = abs(nums[i+1]-nums[i])
    elif nums[i+1]-nums[i] == lowestDiff:
        res.append(nums[i])
        res.append(nums[i+1])

print(*res)

one simple algorithm:
0. get the inputs from console
1. sort the input array as sortedInput
2. set lowestDiff to maximum integer value
3. set resultArray to empty array
4. for i = 1 to length of sortedInput-1
    4a. delta = absolute value (sortedInput[i] - sortedInput[i-1])
    4b. if delta < lowestDiff, then
        -> lowestDiff = delta
        -> clear resultArray (remove all elements from array)
        -> add to resultArray sortedInpit[i-1], and then sortedInput[i]
4c. Else, if delta == lowestDiff, then
        -> add to resultArray sortedInpit[i-1], and then sortedInput[i]
5. print resultArray as space-separated integer on single line.

For those who are getting Test Case 3 & 4 wrong and their code is correct, you need to output the pairs in ascending order.

Python3 solution All test cases passed

def closestNumbers(arr):
    sorted_arr = sorted(arr)
    diff = []
    for i in range(len(sorted_arr) - 1):
        diff.append(sorted_arr[i+1] - sorted_arr[i])
    value = min(diff)
    result = []
    for i in range(len(sorted_arr) - 1):
        if (sorted_arr[i+1] - sorted_arr[i]) == value:
            result.append(sorted_arr[i])
            result.append(sorted_arr[i+1])
    return result