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.
for _ in range(int(input())):
    a,b=map(int,input().split())
    r=0
    if a==b:
        t=a//3
        l=a%3
        if l == 2:
            print(2*t+1)
        else:
            print(2*t)
    elif a > b:
        fark=a-b
        r+=fark
        a-=2*fark
        b-=fark
        if a == 0:
            print(r)
        elif a >0:
            t=a//3
            l=a%3
            if l == 2:
                print(2*t+1+r)
            else:
                print(2*t+r)
        else:
            u=-b
            print(r-u)






    else:
        fark=b-a
        r+=fark
        a-=fark
        b-=2*fark
        if a == 0:
            print(r)
        elif a >0:
            t=a//3
            l=a%3
            if l == 2:
                print(2*t+1+r)
            else:
                print(2*t+r)
        else:
            u=-a
            print(r-u)
