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 solve_test_case(t):
    a, b = parse_array(int)

    def f(a, b):
        diff = b - a
     
        v = a - diff
        if v < 0:
            print(a)
        else:
            d = (v // 3) * 2
            v = v % 3
            if v == 2:
                d += 1
            print(d + diff)

 
    f(min(a, b), max(a, b))
 

def parse_array(f):
    return list(map(f, input().split()))

def solve():
    T = int(input())

    for t in range(T):
        solve_test_case(t)

if __name__ == "__main__":
    solve()
