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())
def ans(a,b):
    
    
    if((a<1 or b<1)):
        return 0
    if(a==1 and b==1):
        return 0
    if(min(a,b)==abs(a-b)):
        return abs(a-b)
    if(min(a,b)<abs(a-b)):
        return min(a,b)
    else:
        diff = abs(a-b)
        p = min(a,b) - diff
        if(p==1 or p==0):
            return diff
        return abs(a-b) + int((2*p)/3)
    
        
        
        
        
        
    
for qq in range(t):
    
    a,b = map(int , input().split())
    print(ans(a,b))
    
        
    
    
    
    




