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())

def solve():
    [A,B] = list(map(int,input().split()))

    A,B = min(A,B),max(A,B)
    delta = min(A,B-A)
    A -= delta
    B -= 2*delta

    ans = delta

    if A % 3 == 0:
        ans += 2*A//3
    elif A % 3 == 1:
        ans += 2*A//3
    elif A % 3 == 2:
        ans += 2*(A-2)//3+1
    return ans

for _ in range(T):
    print(solve())
