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.
for t in range(int(input())):
	a,b=map(int,input().split())
	if a<2 and b<2:
		print(0)
	elif a==0 or b==0:
		print(0)
	else:
		ans=0
		if abs(a-b)>=min(a,b):
			ans+=min(a,b)
			print(ans)
		else:
			if a==min(a,b) and a!=b:
				ans+=(b-a)
				a=a-(b-a)
				b=b-2*(b-a)
				while a>=3:
					ans+=2*(a//3)
					a=a%3
					b=a
				if a==2:
					ans+=1
			elif b==min(a,b) and a!=b:
				ans+=(a-b)
				a=a-2*(a-b)
				b=b-(a-b)
				while a>=3:
					ans+=2*(a//3)
					a=a%3
					b=a
				if a==2:
					ans+=1
			else:
				while a>=3:
					ans+=2*(a//3)
					a=a%3
					b=a
				if a==2:
					ans+=1
			print(ans)