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.
'''input
4
4 4
1000000000 0
7 15
8 7



'''
 
 
from bisect import bisect_right as bl
from random import randint as R
RI = lambda : [int(_x) for _x in raw_input().split()]




for _ in range(input()):
	a,b = RI()

	if a>b:
		a,b = b,a


	if 2*a<b:
		print a
	else:
		x = (b-a)
		a = a-x
		b = b-2*x


		print x + (a/3)*2 + int(a%3==2)
