Maximum Height of a Triangle

You are given two integers red and blue representing the count of red and blue colored balls. You have to arrange these balls to form a triangle such that the 1st row will have 1 ball, the 2nd row will have 2 balls, the 3rd row will have 3 balls, and so on.

All the balls in a particular row should be the same color, and adjacent rows should have different colors.

Return the maximum height of the triangle that can be achieved.

 

Example 1:

Input: red = 2, blue = 4

Output: 3

Explanation:

The only possible arrangement is shown above.

Example 2:

Input: red = 2, blue = 1

Output: 2

Explanation:


The only possible arrangement is shown above.

Example 3:

Input: red = 1, blue = 1

Output: 1

Example 4:

Input: red = 10, blue = 1

Output: 2

Explanation:


The only possible arrangement is shown above.

 

Constraints:

Example Testcases:

2
4
2
1
1
1
10
1