CF1148A.Another One Bites The Dust

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 $a$ strings "a", $b$ strings "b" and $c$ 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?

我们称一个字符串是“好”的，当且仅当它仅由两种字母——‘a’ 和 ‘b’ 组成，且任意两个相邻字母均不相同。例如，“baba” 和 “aba” 是好字符串，而 “abb” 是坏字符串。

你有 $a$ 个字符串 “a”、$b$ 个字符串 “b” 以及 $c$ 个字符串 “ab”。你需要从中选出某个子集，并以任意顺序将它们连接起来。

通过这种方式，你能得到的最长的好字符串的长度是多少？

The first line contains three positive integers $a$, $b$, $c$ ($1 \leq a, b, c \leq 10^9$) — the number of strings "a", "b" and "ab" respectively.

第一行包含三个正整数 $a$、$b$、$c$（$1 \leq a, b, c \leq 10^9$），分别表示字符串 "a"、"b" 和 "ab" 的数量。

Print a single number — the maximum possible length of the good string you can obtain.

输出一个整数——你能得到的“好字符串”的最大可能长度。

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".

在第一个例子中，最优字符串是 "baba"。

在第二个例子中，最优字符串是 "abababa"。

在第三个例子中，最优字符串是 "bababababab"。

在第四个例子中，最优字符串是 "ababab"。