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 _ in range(T):
    a,b=map(int,input().split())
    c=0
    if(a==b):
        print((a+b)//3)
    elif(a==0 or b==0):
        print('0')
    else:
         if(max(a,b)//2>=min(a,b)):
            print(min(a,b))
            c+=1
         else:
            if(max(a,b)%2==0):
                a1=(max(a,b)//2)
            else:
                y=max(a,b)//2
                if(min(a,b)-y>1):
                    a1=(y+1)
                else:
                    a1=(y)
         t=min(a,b)
         y=2*t
         s=max(a,b)-min(a,b)
         if(y%3==1 and s>1):
             b1=((y//3)+1)
         elif(y%3==2 and s>0):
             b1=((y//3)+1)
         else:
            b1=(y//3)
         if(c==0):   
             print(max(a1,b1))              
