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 result(a,b):
        MIN=min(a,b)
        MAX=max(a,b)
        ans1=0
        if MAX>=2*MIN:
            return MIN
        ans=(MIN//3)*2
        MAX-=3*(MIN//3)
        MIN=MIN%3 
        MAX=max(MAX,MIN)
        MIN=min(MAX,MIN)
        if MIN==1 and MAX>=2:
            ans+=1 
        elif MIN==2 and MAX>=6:
            ans+=2 
        elif MIN==2 and MIN<=MAX<6:
            ans+=1 
        return max(ans,ans1,(a+b)//3)
t=int(input())
for i in range(t):
    a,b=map(int,input().split()) 
    if a==0 or b==0:
        print(0)
    else:
        print(result(a,b))