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
#input = sys.stdin.readline
def solve():
    a, b = map( int, input().split())
    if a > b:
        a, b = b, a
    c = min(b-a,a)
    ans = c
    a -= c
    b -= c*2
    d = min(a,b)
    e = d//3
    ans += e*2
    a -= e*3
    b -= e*3
    if a >= 1 and b >= 2:
        ans += 1
        a -= 1
        b -= 2
    if a >= 2 and b >= 1:
        ans += 1
        a -= 1
        b -= 1
    return ans
    

def main():
    T = int( input())
    for _ in range(T):
        print(solve())
if __name__ == '__main__':
    main()
