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.

if(__name__ == '__main__'):
    test = int(input())
    while(test > 0):
        test -= 1
        a, b = map(int, input().split())
        if(a > b):
            temp = b
            b = a
            a = temp
        x = b - a
        if(x > a):
            print(a)
        else:
            ans = x
            a -= x
            b -= 2 * x
            ans += ( a // 3 ) * 2
            a = a % 3
            if(a > 1):
                ans += 1
            print(ans)
        print('\n')