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.
t = int(input())
while t > 0:
    a, b = [int(c) for c in input().split()]
    emerald = 0
    if a == 0 or b == 0:
        emerald = 0
    elif a >= 2 * b:
        emerald = b
    elif b >= 2 * a:
        emerald = a
    else:
        if a > b:
            emerald += (a - b)
            a = 2 * b - a
            if a % 3 == 0 or a % 3 == 1:
                emerald += 2 * (a // 3)
            else:
                emerald += 2 * (a // 3) + 1
        else:
            emerald += (b - a)
            b = 2 * a - b
            if b % 3 == 0 or b % 3 == 1:
                emerald += 2 * (b // 3)
            else:
                emerald += 2 * (b // 3) + 1
    print(emerald)
    t -= 1
