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 program():
    a,b=map(int, input().split())
    if b<a:
        b,a=a,b

    d=b-a
    if a<=b//2:
        print(a)
    elif a==b:
        di={1:0,2:1,3:2}
        count=0
        if a<=3:
            count+=di[a]
        else:
            if a%3==0:
                count+=2*(a//3)
            else:
                count+=2*(a//3) + di[a%3]


        print(count)
    else:
        a-=d
        di = {1: 0, 2: 1, 3: 2}
        b-=2*d
        count=d
        if a<=3:
            count+=di[a]
        else:
            if a%3==0:
                count+=2*(a//3)
            else:
                count+=2*(a//3) + di[a%3]
        print(count)



for i in range(int(input())):
    program()