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 main():
    import sys
    sys.setrecursionlimit(10**6)
    input = sys.stdin.readline
    t = int(input())
    for _ in range(t):
        a, b = [int(x) for x in input().strip().split()]
        if b < a:
            a, b = b, a
        ans = 0
        ans += min(a, b - a)
        a -= ans
        b -= 2 * ans
        if a >= 3 and b >= 3:
            t = min(a, b) // 3
            ans += 2 * t
            a -= 3 * t
            b -= 3 * t
        if a >= 2 and b >= 1:
            ans += 1
            a -= 2
            b -= 1
        if b >= 2 and a >= 1:
            ans += 1
        print(ans)

if __name__ == '__main__':
    main()