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.
import sys
input=sys.stdin.buffer.readline

t=int(input())
while t:
	t-=1
	a,b=map(int,input().split())
	c=max(a,b)
	d=min(a,b)
	if c>=2*d:
		print(d)
	else:
		print((c+d)//3)
"""
	else:
		if d>(c//2):

			if c-c//2>0 and d-(c//2)>=2:
				print((c//2)+1)
			else:
				print(c//2)
		else:
			print(d)

"""