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.
n=int(input())
for _ in range(n):
    c=0
    x,y=list(map(int,input().split()))
    while (x>0 and y>0) and not(x==1 and y==1):
        x,y=max(x,y),min(x,y)
        if x==2 and y==1:
            c+=1
            break
        a=round(x/2)
        b=a//2
        if b<y:
            c+=b
            y-=b
            x-=a
        else:
            c+=y
            break
        
    print(c)
        




