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())

for i in range(t):

	a,b = map(int,input().split())
	if a == 0 or b == 0:
		print(0)
	elif 2*a <= b:
		print(a)
	elif 2*b <= a:
		print(b)
	else:
		if b > a:
			# b - 2*x = a - x
			x = b - a 
			ans = x
			a = a - x
			if a%3 == 2:
				ans = ans + 1 + 2*int(a/3)
			else:
				ans = ans + 2*int(a/3)
		elif a >= b:
			x = a - b		
			ans = x
			b = b - x
			if b%3 == 2:
				ans = ans + 1 + 2*int(b/3)
			else:
				ans = ans + 2*int(b/3)
		print(ans)