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())
for t in range(T):
    a, b = list(map(int, input().split()))

    mini, maxi = min([a, b]), max([a, b])

    # On veut avoir mini == maxi, en attendant on prend 2 maxi pour un mini
    diff = maxi - mini

    first_item = min(diff, mini)

    res = first_item
    mini -= first_item
    maxi -= 2 * first_item
    mini, maxi = min(mini, maxi), max(mini, maxi)
    if mini != 0:
        r = mini // 3
        res += 2 * r
        mini -= 3 * r
        maxi -= 3 * r
        while mini > 0:
            if maxi >= 2 * mini:
                res += mini
                break
            mini -= 1

    print(res)


# T = int(input())
# for t in range(T):
#     a, b = list(map(int, input().split()))

#     mini, maxi = min([a, b]), max([a, b])

#     res1 = min(mini, maxi // 2)
#     res2 = 2 * (mini // 3)
#     # print(res1, res2)
#     # print(mini, maxi)
#     if (mini % 3) > 0:
#         d = mini % 3
#         # print("d : ", d)
#         while d > 0:
#             if maxi >= mini + d:
#                 res2 += d
#                 break
#             d -= 1

#     print(max(res1, res2))
