Let's call a string good if and only if it consists of only two types of letters — 'a' and 'b' and every two consecutive letters are distinct. For example "baba" and "aba" are good strings and "abb" is a bad string.
You have aa strings "a", bb strings "b" and cc strings "ab". You want to choose some subset of these strings and concatenate them in any arbitrarily order.
What is the length of the longest good string you can obtain this way?
The first line contains three positive integers aa, bb, cc (1≤a,b,c≤10^91≤a,b,c≤10^9) — the number of strings "a", "b" and "ab" respectively.Multiply Tests.
1 1 1
2 1 2
3 5 2
2 2 1
1000000000 1000000000 1000000000
4
7
11
6
4000000000
In the first example the optimal string is "baba".
In the second example the optimal string is "abababa".
In the third example the optimal string is "bababababab".
In the fourth example the optimal string is "ababab".