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.
from sys import stdin,stdout
for query in range(int(stdin.readline())):
    ab=stdin.readline().split()
    a=int(ab[0])
    b=int(ab[1])
    if a>=2*b:
        stdout.write(str(b)+'\n')
    elif b>=2*a:
        stdout.write(str(a)+'\n')
    else:
        if b>a:
            (b,a)=(a,b)
        total=0
        total+=a-b
        b-=total
        a-=2*total
        total+=(a//3)*2
        a=a%3
        b=b%3
        if a>=2:
            total+=1
        stdout.write(str(total)+'\n')