Polycarp plays a well-known computer game (we won't mention its name). In this game, he can craft tools of two types — shovels and swords. To craft a shovel, Polycarp spends two sticks and one diamond; to craft a sword, Polycarp spends two diamonds and one stick.

Each tool can be sold for exactly one emerald. How many emeralds can Polycarp earn, if he has a sticks and b diamonds?

Input

The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.

The only line of each test case contains two integers a and b (0 ≤ a, b ≤ 10^9) — the number of sticks and the number of diamonds, respectively.

Output

For each test case print one integer — the maximum number of emeralds Polycarp can earn.

Example

Input


4
4 4
1000000000 0
7 15
8 7


Output


2
0
7
5

Note

In the first test case Polycarp can earn two emeralds as follows: craft one sword and one shovel.

In the second test case Polycarp does not have any diamonds, so he cannot craft anything.
t=int(input())
for _ in range(t):
    A,B=map(int,input().split())
    if A==0 or B==0:
        print(0)
    else:
        print((A+B)//2)

#     c1=0
#     a=A
#     b=B
#     while a>=2 and b>=1:
#         a-=2
#         b-=1
#         c1+=1
#     # print(a,b,c1)
#     while a>=1 and b>=2:
#         a-=1
#         b-=2
#         c1+=1
#     # print(a,b,c1)
#     c2=0
#     a=A
#     b=B
#     while a>=1 and b>=2:
#         a-=1
#         b-=2
#         c2+=1
#     # print(a,b,c2)
#     while a>=2 and b>=1:
#         a-=2
#         b-=1
#         c2+=1
#     # print(a,b,c2)
#     if c1>c2:
#         print(c1)
#     else:
#         print(c2)
