class Solution:
 def secondGreaterElement(self, nums: List[int]) -> List[int]:
 total_nums = len(nums)
 second_next_greater = [-1] * total_nums
 # Decreasing monotonic stacks: (num, idx).
 stack_1, stack_2 = [(nums[0], 0)], []
 # Increasing monotonic list to transport tuples from stack 1 to stack 2.
 transporter = []
 for current_idx in range(1, total_nums):
 while stack_2 and stack_2[-1][0] < nums[current_idx]:
 _, past_idx = stack_2.pop(-1)
 second_next_greater[past_idx] = nums[current_idx]
 while stack_1 and stack_1[-1][0] < nums[current_idx]:
 transporter.append(stack_1.pop(-1))
 
 stack_2.extend(transporter[::-1]) # Ensure decreasing monotonicity.
 transporter.clear()
 stack_1.append((nums[current_idx], current_idx))
 return second_next_greater