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.
t = int(input())
TestCases = []
for test in range(0,t):
	entry = input().split(' ')
	entry[0] = int(entry[0])
	entry[1] = int(entry[1])
	TestCases.append(entry[:2])

for test in TestCases:
	Emerland = 0
	# exclude 0 in (a,b) or  a+b < 3 (can't form any sword or shovel)
	if ( 0 in test ) or sum(test)<3:
		print(0)
		continue
	# If a or b is 1 or their sum < 5 then we can only make one sword or shovel.
	elif (sum(test)<6) or (1 in test):
		print(1)
		continue
	elif ( 2 in test):
		print(2)
		continue
	# if the sum a,b>=6
	else:
		if test[0] < test[1]:
			test[0],test[1] = test[1],test[0]

		if test[0] >= 2*test[1]:
			Emerland = test[1]
		else:
			Emerland = Emerland + int(test[0]/3) + int(test[1]/3)
			test[0] = test[0]%3
			test[1] = test[1]%3

			if (test[0]!=0 and test[1]!=0) and (test[0]+test[1]>=3):
				Emerland = Emerland + 1

		print(Emerland)