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.
def code(a,b):
    if a == 0 or b == 0:
        print(0)
        return
    
    res = 0
    
    if a//b > 1 or b // a > 1 :
        print(min(a,b))
        return
    
    res = min(a//3,b//3)
    
    a = a - res*3
    b = b - res*3
    
    res = 2*res
    
    
    if (a!=0 and b!= 0) and (a//b > 1 or b // a > 1) :
        res += min(a,b)
        
    if (a == 2 or a == 3) and (b == 3 or b == 2):
        res +=1
    
    print(res)

	
if __name__ == "__main__":
    t = int(input())
    for i in range(t):
        a,b = list(map(int,input().rstrip().split()))
        code(a,b)