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 emeralds(min_val, max_val):
    if max_val >= 2 * min_val:
        return min_val
    else:
        count = 0
        diff = max_val - min_val
        count += diff
        max_val -= 2 * diff
        min_val -= diff
        pairs = min_val // 3
        count += pairs * 2
        min_val -= pairs * 3
        max_val -= pairs * 3
        if min_val == 2:
            count += 1
        return count

t_test = int(input().strip())
while t_test > 0:
    a, b = list(map(int, input().strip().split(' ')))
    min_val = min(a, b)
    max_val = max(a, b)
    print(emeralds(min_val, max_val))
    t_test -= 1