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())

for _ in range(N):
	a,b = map(int,input().split())
	res=0
	sim=0
	if (a == 0) or (b == 0):
		print(0)
		continue
	if a>b:
		if 2*b <= a:
			print(b)
			sim = 1
	else:
		if 2*a <= b:
			print(a)
			sim = 1

	if sim:
		continue
	if a > b:
		aux = a-b
		print(aux+((2*(b-aux))//3))
	else:
		aux = b-a
		print(aux+((2*(a-aux))//3))

