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  
  
def main(): 
	N = int(stdin.readline().rstrip())
	for tc in range(N): 
		a, b  = [int(x) for x in stdin.readline().split()] 
		if min(a, b) * 2 <= max(a,b):
			stdout.write(str(min(a,b))+'\n')
			continue
		aa = (a / 3)
		bb = (b / 3)
		ans = min(aa, bb)
		a -=(ans*3)
		b -=(ans*3)
		ans = ans*2
		if (a ==1  and b > 1 )or ( a > 1 and b == 1):
			ans +=1
		elif (a ==2  and b > 3 )or ( a > 3 and b == 2):
			ans +=2
		elif (a ==2  and b <= 3 )or ( a<= 3 and b == 2):
			ans +=1

		stdout.write(str(ans)+'\n')
if __name__ == "__main__": 
	main()