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())
ans = []
for i in range(t):
	a, b = map(int, input().split())
	if (a == b):
		ans.append(a//2)
		continue
	mult = 1

	while(a//10 > 1 or b//10 > 1):
		a /= 10
		b /= 10
		mult *= 10

	emeralds = 0
	while ((a >= 2 and b >= 1) or (b >= 2 and a >= 1)):
		if (a > b):
			a -= 2
			b -= 1

		else:
			a -= 1
			b -= 2
		emeralds += 1
	ans.append(emeralds*mult)

for i in range(t):
	print(ans[i])