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.
a=int(input())
for i in range(0,a):
    a,b=map(int,input().split())
    arr=[a,b]
    arr.sort()
    ans=arr[1]-arr[0]
    arr[0]=arr[0]-ans
    arr[1]=arr[1]-2*ans
    if(arr[0]<0):
        print(min(max(a,b)//2,min(a,b)))
    else:
        if(arr[0]%3==0):
            print(2*arr[0]//3+ans)
        elif(arr[0]%3==1):
            print(2*arr[0]//3+ans)
        else:
            print(2*arr[0]//3+ans)
        
        