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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
using namespace std; 
 
int main () {
  int N; cin >> N;
  vector<int> H(N);
  for(int i = 0; i < N; ++i) {
    cin >> H[i];
  }
  
  int ans = 0;
  for(int i = 0; i < N; ++i) {
    bool is_candidate = true;
    for ( int j = 0; j < i; ++j ) {
      if ( H[j] > H[i]) {
        is_candidate = false;
        break;
      }
      if (is_candidate) {
        ++ans;
      }
    }
  }
  cout << ans << endl;
}