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.
for _ in range(int(input())):
  a,b=map(int,input().split())
  c=0
 # if (a==0 or b==0 ) or (a<2 and b<2):
  #  print('0')
  if  max(a,b)>((min(a,b)*2)):
    print(min(a,b))
  else:
    print(int((a+b)/3))
     #while(True):
    # :
     # print(c)
      #break;
    #else:
     # t1=max(a,b)-2
      #t2=min(a,b)-1
      #print(t1,t2)
      #a=t1
      #b=t2
      #c+=1