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 find(x,y):
    if(x==0 or y==0 or(x==1 and y==1)):
        return(0)
    elif(x*2<=y):
        return(x)
    elif(y*2<=x):
        return(y)
    else:
        if(x>y):
            w=y//2
            return(w+find(x-(2*w),y-(w)))
        else:
            w=x//2
            return(w+find(y-(2*w),x-w))
for _ in range(int(input())):
    x,y=map(int,input().split())
    print(find(x,y))
                   