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_LINES = sys.stdin.read().splitlines()
input = iter(_INPUT_LINES).__next__

tc = int(input()) 

for zz in range(tc):
	a,b = map(int,input().split())

	if(b < a):
		a,b = b,a 

	m = b - a 
	if(m >= a):
		print(a)
	else :
		a -= m 
		n = (2*a) // 3
		print(m+n)

	# ans = 0
	# while (True):
	# 	if(a < 1 or b < 2):
	# 		break 
	# 	b -= 2 
	# 	a -= 1 
	# 	ans += 1
	# 	if(b < a):
	# 		a,b = b,a
	# print(ans)
