Construct the Longest New String
You are given three integers x, y, and z.
You have x strings equal to "AA", y strings equal to "BB", and z strings equal to "AB". You want to choose some (possibly all or none) of these strings and concatenate them in some order to form a new string. This new string must not contain "AAA" or "BBB" as a substring.
Return the maximum possible length of the new string.
A substring is a contiguous non-empty sequence of characters within a string.
Example 1
Input
x = 2, y = 5, z = 1Output
12Concatenating "BB", "AA", "BB", "AA", "BB", and "AB" forms "BBAABBAABBAB" with length 12, and it is impossible to construct a longer valid string.
Example 2
Input
x = 3, y = 2, z = 2Output
14Concatenating "AB", "AB", "AA", "BB", "AA", "BB", and "AA" forms "ABABAABBAABBAA" with length 14, and it is impossible to construct a longer valid string.
Constraints
- 1 <= x, y, z <= 50