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.
def shovels_and_swords(a,b):
	equal = False
	if a == b:
		equal = True
	bigger = max(a,b)
	smaller = min(a,b)
	if equal:
		product = a/1.5
		product = int(product)

	else:
		difference = bigger - smaller
		if smaller >= difference:
			leftover = smaller- difference
			product = difference + int(leftover/1.5)
		else:
			product = smaller

	return product
t = int(input())
answers = []
for test in range(t):
	a,b = (int(x) for x in input().split())
	ans = shovels_and_swords(a,b)
	answers.append(ans)
for ans in answers:
	print(ans)