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 calc(i, j):
    if i == 0 or j == 0:
        return 0
    if 2 * j < i or 2 * i < j:
        return min(i, j)
    if (i == 2 and j == 1) or (i == 1 and j == 2) or (i == 2 and j == 2):
        return 1
    elif (i == 0 and j == 1) or (i == 0 and j == 2) or (i == 1 and j == 0) or (
            i == 1 and j == 1) or (i == 2 and j == 0):
        return 0
    h = int(i / 3) + int(j / 3)
    return h + calc(i % 3, j % 3)


t = int(input())
while t:
    a, b = map(int, input().split())
    print(calc(a, b))
    t = t - 1