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.
n = int(input())
for k in range(n):
    a, b = map(int, input().split())
    if a >= b * 2:
        print(b)
    elif b >= a * 2:
        print(a)
    else:
        a, b = max(a, b), min(a, b)
        d = a - b
        a -= 2 * d
        b -= d
        r = d
        pr = min(a//3, b//3)
        a -= pr * 3
        b -= pr * 3
        pr *= 2
        while (a >= 2 and b >= 1) or (a >= 1 and b >= 2):
            if a >= 1 and b >= 2:
                pr += 1
                a -= 1
                b -= 2
            elif a >= 2 and b >= 1:
                pr += 1
                a -= 2
                b -= 1
        print(r + pr)
    
    
