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.
t=int(input())
while(t):
  a,b=map(int,input().split())
  c=max(a,b)
  d=min(a,b)
  if(c>=2*d):
    print(d)
  else:
    ans=0
    while(c>d):
     # print(c,d)
      ans+=c-d
      c=c-2*(ans)
      d=d-(ans)
    #  print(ans)
      ##print(c,d)
   # print(c,d)
    if(c>=3):
      h=c//3
      d-=h*3
      c-=h*3
      ans+=2*h
    if(c==2 and d>=4):
      #print(c,d)
      ans+=2
    if(d<4 and d>1 and c>0):
      ans+=1
    print(ans)
  t-=1