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.
tests = int(input())
for i in range(tests):
    numbers = input().split(" ")
    a = int(numbers[0])
    b = int(numbers[1])
    res = 0

    if a < b:
        temp = a
        a = b
        b = temp

    if a >= 2 * b:
        print(b)
    else:
        res += a - b
        draw = b - res
        if draw % 3 <= 1:
            res += (draw // 3) * 2
            print(res)
        else:
            res += (draw // 3) * 2 + 1
            print(res)