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 t in range (int(input())):
    a,b=map(int,input().split())
    diamonds=0
    if(b>=(2*a) or a>=2*b):
        diamonds+=min(a,b)
        print(diamonds)
        continue
    m1=min(a,b)
    q=m1//3
    diamonds+=q*2
    a1=a-q*3
    b1=b-q*3
    if(a1==1 and b1==2):
        diamonds+=1
    elif(a1==2 and b1==1):
        diamonds+=1
    elif(a1==2 and b1==2):
        diamonds+=1
    print(diamonds)