# Given an array with n objects colored red, white or blue, sort them in-place so that objects of the same color are adjacent, with the colors in the order red, white and blue.

# Here, we will use the integers 0, 1, and 2 to represent the color red, white, and blue respectively.

# Note: You are not suppose to use the library's sort function for this problem.

# Example:

# Input: [2,0,2,1,1,0]
# Output: [0,0,1,1,2,2]
# Follow up:

# A rather straight forward solution is a two-pass algorithm using counting sort.
# First, iterate the array counting number of 0's, 1's, and 2's, then overwrite array with total number of 0's, then 1's and followed by 2's.
# Could you come up with a one-pass algorithm using only constant space?

class Solution:
    def sortColors(self, nums: List[int]) -> None:
        """
        Do not return anything, modify nums in-place instead.
        """
        # nx is pointing to the end of the subarrayx
        n0 = -1
        n1 = -1
        n2 = -1
        for i in range(len(nums)):
            if nums[i] == 0:
                n2 += 1
                n1 += 1
                n0 += 1
                nums[n2] = 2
                nums[n1] = 1
                nums[n0] = 0
            elif nums[i] == 1:
                n2 += 1
                n1 += 1
                nums[n2] = 2
                nums[n1] = 1
            elif nums[i] == 2:
                n2 += 1
                nums[n2] = 2
