Problem:
Score : 100 points

Problem Statement

There are two buttons, one of size A and one of size B.

When you press a button of size X, you get X coins and the size of that button decreases by 1.

You will press a button twice. Here, you can press the same button twice, or press both buttons once.

At most how many coins can you get?

Constraints

All values in input are integers.

3 \leq A, B \leq 20

Input

Input is given from Standard Input in the following format:

A B

Output

Print the maximum number of coins you can get.

Sample Input 1

5 3

Sample Output 1

9

You can get 5 + 4 = 9 coins by pressing the button of size 5 twice, and this is the maximum result.

Sample Input 2

3 4

Sample Output 2

7

Sample Input 3

6 6

Sample Output 3

12

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

tiles = gets.chop

len = tiles.length
pattern_a = []
pattern_b = []

len.times do |i|
  if i % 2 == 0
    pattern_a.push(1)
    pattern_b.push(0)
  else
    pattern_a.push(0)
    pattern_b.push(1)
  end
end

a_change = 0
b_change = 0

len.times do |i|
  if (tiles[i].to_i ^ pattern_a[i]) == 1
    a_change += 1
  else
    b_change += 1
  end
end

if a_change > b_change
  puts a_change
else
  puts b_change
end