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 solve(a, b):
    if a == 0 or b == 0 or (a, b) == (1, 1):
        return 0
    if (a, b) in [(1, 2), (2, 1), (2, 2)]:
        return 1
    if a == b:
        return 2 * (a//3) + solve(a % 3, a % 3)

    mx = max(a, b)
    mn = min(a, b)
    t = min(mx - mn, mn)

    return t + solve(mx - 2*t, mn - t)

# s1 - (2*n+m) + s2 = s1+s2

# s1 - 2*n - m == 0
# s2 - n - 2*m == 0
# s1 + s2 - 3*n - 3*m == 0
# (s1 + s2)//3 == n + m


# n m

t = int(input())
for _ in range(t):
    a, b = map(int, input().split())
    print(solve(a, b))