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 as_list():
    return list(map(int, input().split()))

def solve():
    [a, b] = as_list()
    solutions = 0
    while True:
        if a == 0 or b == 0:
            return solutions
        if a == b:
            if a == 1:
                return solutions
            if a == 2:
                return 1 + solutions
            x = a // 3
            solutions += 2 * x
            a -= 3 * x
            b -= 3 * x
        if a < b:
            [a, b] = [b, a]
        if 2 * b <= a:
            return solutions + b
        x = (a - b) // 2
        if 2 * x < a - b:
            x += 1
        solutions += x
        a -= 2 * x
        b -= x

if __name__=='__main__':
    [tests] = as_list()
    for _ in range(tests):
        print(solve())