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.
l=int(input())
for i in range(l):
    st=input().split()
    x=int(st[0])
    y=int(st[1])        
    if x<=y:
        temp=x
        x=y
        y=temp
    if x>=2*y:
        print(y)
        continue
    if y+2<x<2*y:
        t=int((y-x%y+2)/3)
        print(y-t)
        continue
    if x>=y:
        z=int(y/3)
        z*=2
        if(y%3==0):
            print(z)
        elif(y%3==1):
            if(x-y>=1):
                print(z+1)
            else:
                print(z)
        else:
            if(x-y)>=2:
                print(z+2)
            else:
                print(z+1)
