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Joysticks ( CodeForces

                                                                  time limit per test 1 second

                                                           memory limit per test 256 megabytes

                                                                        input standard input

                                                                      output standard output

Friends are going to play console. They have two joysticks and only one charger for them. Initially first joystick is charged at a1 percent and second one is charged at a2 percent. You can connect charger to a joystick only at the beginning of each minute. In one minute joystick either discharges by 2 percent (if not connected to a charger) or charges by 1 percent (if connected to a charger).

Game continues while both joysticks have a positive charge. Hence, if at the beginning of minute some joystick is charged by 1 percent, it has to be connected to a charger, otherwise the game stops. If some joystick completely discharges (its charge turns to 0), the game also stops.

Determine the maximum number of minutes that game can last. It is prohibited to pause the game, i. e. at each moment both joysticks should be enabled. It is allowed for joystick to be charged by more than 100 percent.

Input

The first line of the input contains two positive integers a1 and a2 (1 ≤ a1, a2 ≤ 100), the initial charge level of first and second joystick respectively.

Output

Output the only integer, the maximum number of minutes that the game can last. Game continues until some joystick is discharged.

Examples

input

3 5

output

6

input

4 4

output

5

Note

In the first sample game lasts for 6 minute by using the following algorithm:

  • at the beginning of the first minute connect first joystick to the charger, by the end of this minute first joystick is at 4%, second is at 3%;
  • continue the game without changing charger, by the end of the second minute the first joystick is at 5%, second is at 1%;
  • at the beginning of the third minute connect second joystick to the charger, after this minute the first joystick is at 3%, the second one is at 2%;
  • continue the game without changing charger, by the end of the fourth minute first joystick is at 1%, second one is at 3%;
  • at the beginning of the fifth minute connect first joystick to the charger, after this minute the first joystick is at 2%, the second one is at 1%;
  • at the beginning of the sixth minute connect second joystick to the charger, after this minute the first joystick is at 0%, the second one is at 2%.

After that the first joystick is completely discharged and the game is stopped.

題解

題意大致是:小明和小紅開黑打遊戲,兩人各用一部手機,因為小紅是女生不怎麼打遊戲,所以比較菜需要小明帶(並不是攻擊女生。。),也就是說兩人必須同時玩(兩部手機必須都有可以支撐一局遊戲的電),但是兩個人的手機電都不多了,此時,可愛的河神大人給了他們一個充電寶,充電寶只能給一部手機充電,也就是說兩個人的手機,插了充電寶的一局增加1的電,不插則減少2的電。小明很想帶妹炫耀他的技術,所以要玩最長的時間,但這個最長的時間是多少呢?就要苦X的我們來算了。

怎麼算最長的時間呢?很簡單,讓電少的插充電寶,電多的放電就好了嘛。但值得注意的是!一局遊戲要掉2的電,所以至少有一部手機的電要大於等於2

# include <cstdio>
# include <algorithm>
# include <cstring>

using namespace std;

int main()
{
	int a, b;
	scanf("%d%d",&a,&b);
	int mark = 0;
	while(a && b)
	{
		if(a>=2 || b>=2)
		{
			if(a >= b)
			{
				b++;
				a-=2;
				mark++;
			}
			else
			{
				a++;
				b-=2;
				mark++;
			}
		}
		else break;
	}
	printf("%d\n",mark);
	return 0;
 }