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.
a = input()
a = int(a)
for i in range(0, a):
    tools = 0
    b = input()
    b = b.split(' ')
    b[0] = int(b[0])
    b[1] = int(b[1])
    stop = False
    if b[0] * 2 <= b[1]:
        print(b[0])
        stop = True
    elif b[1] * 2 <= b[0]:
        print(b[1])
        stop = True
    if not stop:
        if b[0] > b[1]:
            diff = b[0] - b[1]
            b[1] -= diff
            b[0] -= 2*diff
            tools = diff + int(b[0] * (2/3))
        elif b[0] == b[1]:
            tools = int(b[0] * (2/3))
        elif b[1] > b[0]:
            diff = b[1] - b[0]
            b[0] -= diff
            b[1] -= 2*diff
            tools = diff + int(b[0] * (2/3))

        print(tools)

