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.
from math import *
from sys import stdin,stdout
input=stdin.buffer.readline

t=int(input())

while t>0:
	ans=0
	a,b=[int(x) for x in input().split()]
	if b<a:
		a,b=b,a
	if b>=2*a:
		ans+=a
	else:
		dist=b-a
		if dist>2:
			dist-=2
			ans+=dist
			a=a-dist
			b=b-dist
		x=a
		ans+=((x//3)*2)
		sub=(x//3)*3
		a-=sub
		b-=sub
		if a==1 and b>1:
			ans+=1
		elif a==2 and b<4:
			ans+=1
		elif a==2 and b>=4:
			ans+=2

	print(ans)

	t-=1