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.
n = int(input())

rr = lambda: input()
rri = lambda: int(input())
rrm = lambda: list(map(int, input().split()))

def solve(a,b):
	amt = 0
	if b > a:
		a,b = b,a
	diff = a-b
	amt += diff

	# attempt to do diff from a side
	if b < diff:
		return b
	else:
		a-=diff*2
		b-=diff
		# do pairs of 3 now
		both = min(a // 3, b // 3)
		amt += both*2

		a -= both*3
		b -= both*3

		# rest as a
		resta = min(a//2, b)

		# rest as b
		restb = min(b//2, a)

	return amt + max(resta,restb)

for _ in range(n):
	a,b = rrm()
	print(solve(a,b))
