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())

for _ in range(t):
    a, b = map(int, input().split())

    if a == 0 or b == 0:
        print(0)
        continue
    resu = 0
    while a > 0 and b > 0:
        a,b = max(a,b), min(a,b)
        c = abs(a-b)
        s = c//2
        if s == 0 and a != b:
            resu += 1
            a -= 2
            b -= 1
            continue
        resu += (min(s, b))
        a -= min(s*2,b*2)
        b -= min(s,b)
        if a == b:
            x = a//3
            a -= x*3
            if a == 2:
                resu += 1
            resu += x*2
            break

    print(resu)
    
# zero