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
sys.setrecursionlimit(1000000)
def answer(a,b):
	if a==0 or b==0 or (a<2 and b<2):
		return 0
	elif a==b:
		if a%3==2:
			return ((a//3)*2)+1
		else:
			return (a//3)*2
	elif abs(a-b)==1:
		return 1+ answer(max(a,b)-2,min(a,b)-1)
	else:
		a1=max(a,b)
		b1=min(a,b)
		minNum=min((a1-b1)//2,b1)
		return minNum + answer(a1-(2*minNum), b1-minNum)
t= int(input())
for T in range(t):
	[a,b] = list(map(int, input().split(' ')))
	print(answer(a,b))