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):
    # test all possible candidates for being boundaries of the simplex,
    # and then test some more...
    Ps = [
        (0, 0),
        (a, 0),
        (b, 0),
        (a//2, 0),
        (b//2, 0),
        ((2*b-a) // 3, (2*a-b) // 3)
    ]

    max_res = 0
    for ll, mm in Ps:
        for lll, mmm in [(ll, mm), (mm, ll)]:
            for dl in range(-1, 2):
                for dm in range(-1, 2):
                    l = lll + dl
                    m = mmm + dm
                    if 0 <= l and 0 <= m and  2*l + m <= a and 2*m+l <= b:
                        max_res = max(l+m, max_res)
    return max_res
T = int(input())
for _ in range(T):
    A, B = [int(x) for x in input().split()]
    print(solve(A, B))
