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.
ni=int(input())
for ti in range(ni):
    a,b=map(int,input().split())
    if((a==0 or b==0) or (a==1 and b==1)):
        print("0")
    elif(a==1 or b==1 or (a==2 and b==2)):
        print("1")
    elif(a==b):
        if(a%3==1 or a%3==0):
            print((a//3)*2)
        else:
            print(((a//3)*2)+1)
    elif(a>=(2*b)):
        print(b)
    elif(b>=(2*a)):
        print(a)
    else:
        if(b>a):
            x=b-a
            a=a-x
            b=b-2*x
        else:
            x=a-b
            b=b-x
            a=a-2*x
        if(a%3==1 or a%3==0):
            print(x+((a//3)*2))
        else:
            print(x+((a//3)*2)+1)
            
            
            
        
        
