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(input()):
    a,b=map(int,raw_input().split())
    c,d=a,b
    p=min(a,b)
    ans=2*(p/3)
    a-=p
    b-=p
    if (a>1 or b>1) and ( a and b):
        ans+=1
    
     

    a,b=c,d
    if (a>=(2*b)) or (b>=(2*a)):
        ans=max(ans,min(a,b))
    print ans
    continue
    if (2*a-b)%3==0 and (2*b-a)%3==0 and (2*a-b)>=0 and (2*b-a)>=0:
         print (2*a-b)/3+(2*b-a)/3
         continue
    c,d=a,b
    ans=0
    t=min(a/2,b)
    ans+=t
    a-=(2*t)
    b-=t
    ans+=min(b/2,a)
    j=ans
   
    ans=0
    a,b=d,c
    
    t=min(a/2,b)
    ans+=t
    a-=(2*t)
    b-=t
    ans+=min(b/2,a)
    print max(j,ans) 