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.
import sys



def solve(s,d):
    if s > d:
       t = s
       s = d
       d = t

    if s < d:
       if d >= 2*s:
           return s
       else:
           diff = d-s
           em = diff
           d -= em
           s -= em
           em += 2*(s//3) + (1 if s%3==2 else 0)
           return em
    else: # equal
       return 2*(s//3) + (1 if s%3==2 else 0)
        


if __name__ == '__main__':
    IN = [x.strip() for x in sys.stdin.readlines()]

    T = int(IN[0])
    for ti in range(T):
        s,d = [int(x) for x in IN[1+ti].split(' ')]
        result = solve(s,d)
        print(result)

