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 f(a,b):
	if b < a:
		return f(b,a)


	gap = min(a, (b- a) / 2, b/2)

	if gap > 0:
		return gap + f(a - gap, b - 2 * gap)
	elif gap == 0:
		r = (min(a,b))/3
		
		res = r *2
		a -= 3*r
		b -= 3*r
		if a:
			if b >= 2:
				a-=1
				b-=2
				res+=1
		if b:
			if a >= 2:
				b-=1
				a-=2
				res+=1
		return res

for _ in range(int(raw_input())):
	print f(*map(int,raw_input().split(' ')))