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 f2(inp):
    a = int(inp[0])
    b = int(inp[1])
    res = 0
    if a == 0 or b == 0:
        return res
    
    if a < 2 and b < 2:
        return res

    high = max([a,b])
    low = min([a,b])
    diff = high - low
    if low < diff:
        diff = low

    if diff > 2:
        low -= diff
        high -=2*diff
        res += diff
    
    #low = high +- 1

    if high == 0 or low == 0:
        return res
    
    if high < 2 and low < 2:
        return res
    
    if low > high:
        high, low = low, high
    

    if low == high == 4:
        res += 2
    else:
        res += int(high / 2) + 1
    
    return res
    
        
            
    


if __name__ == "__main__":
    test = input()
    for e in range(int(test)):
        print(f2(input().split(" ")))