ACM ICPC is launching a thick burger. The thickness (or the height) of a piece of club steak is $A$ ($1\le A\le 100$). The thickness (or the height) of a piece of chicken steak is $B$ ($1\le B\le 100$).

The chef allows to add just three pieces of meat into the burger and he does not allow to add three pieces of same meat. As a customer and a foodie, you want to know the maximum total thickness of a burger which you can get from the chef. Here we ignore the thickness of breads, vegetables and other seasoning.

Input

The first line is the number of test cases. For each test case, the first line contains two positive integers $A$ and $B$.

Output

For each test case, output a line containing the maximum total thickness of a burger.

Example

Input

3
68 42
1 35
25 70

Output

178
71
165