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())
result = []

for i in range(t):
    a = [int(x) for x in input().split(" ")]
    kc = min(abs(a[0] - a[1]), a[0], a[1])
    if a[1] > a[0]:
        a[1] = a[1] - 2 * kc
        a[0] = a[0] - kc
    else:
        a[1] = a[1] - kc
        a[0] = a[0] - 2 * kc

    if a[0] > 0 and a[1] > 0:
        du = a[0] % 3
        chia = int(a[0] / 3)
        if du == 2:
            result.append(kc + chia * 2 + 1)
        else:
            result.append(kc + chia * 2)
    else:
        result.append(kc)

for i in result:
    print(i)
