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.
numberOfCases= int(input())

testCases = []
for case in range(0, numberOfCases):
	sticks, diamonds = input().split(' ')
	testCases.append([int(sticks),int(diamonds)])

for [sticks, diamonds] in testCases:
	# exclude 0 in (a,b) or  a+b < 3 (can't form any sword or shovel)
	if ( 0 in [sticks, diamonds] ) or (sum([sticks, diamonds]) < 3):
		print(0); continue
	# If a or b is 1 or their sum < 5 then we can only make one sword or shovel.
	if (sum([sticks, diamonds]) < 6) or (1 in [sticks, diamonds]):
		print(1); continue

	
	if sticks < diamonds:
		sticks,diamonds = diamonds,sticks

	if sticks >= 2*diamonds:
		print(diamonds); continue
	
	Emerland = 0
	Emerland = int(sticks/3) + int(diamonds/3)
	sticks, diamonds = sticks%3, diamonds%3

	if (sticks!=0 and diamonds!=0) and (sticks+diamonds>=3):
		print(Emerland + 1); continue

	print(Emerland)