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 i in range(t):
    n=list(map(int,input().split()))
    a=n[0]
    b=n[1]
    if(a>=2*b):
        print(b)
    elif(b>=2*a):
        print(a)
    elif(a<b):
        temp=a*2 - b
        if(temp%3==0):
            t = temp//3 
        else:
            t= temp//3 + 1

        print(a-t)
    elif(b<a):
        temp=b*2 - a
        if(temp%3==0):
            t = temp//3 
        else:
            t= temp//3 + 1
        print(b-t)

    elif(a==b):
        print((a+b)//3)

