Given an array nums 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.

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

You must solve this problem without using the library's sort function.

Examples

Example 1

Input:  nums = [2,0,2,1,1,0]
Output: [0,0,1,1,2,2]

Example 2

Input:  nums = [2,0,1]
Output: [0,1,2]

Example 3

Input:  nums = [1]
Output: [1]

Constraints

• 1 <= nums.length <= 300
• nums[i] is either 0, 1, or 2

Follow-up

Could you come up with a one-pass algorithm using only constant extra space?

How the tests work: the answer is checked by reading your modified input, not your return value.