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.
for _ in range(int(input())):
    a, b = map(int, input().split())
    l = 0
    r = min(a, b)+1
    x = 0
    while r - l > 1:
        m = (r + l) // 2
        m1 = m + 1
        if m + min(a - 2*m, (b-m)//2) > m1 + min(a - 2*m1, (b-m1)//2):
            x = m + min(a - 2*m, (b-m)//2)
            r = m
        else:
            l = m
    print(max(l + min(a - 2*l, (b-l)//2), r + min(a - 2*r, (b-r)//2), min(a, b // 2), min(a // 2, b)))
