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 > 0):
  a, b = [int(x) for x in input().split()]
  res = 0
  if (a * 2 < b):
    crafted = a
    res = crafted
    a -= crafted
    b -= crafted*2
  elif (b * 2 < a):
    crafted = b
    res = crafted
    b -= crafted
    a -= crafted*2
  mn = min(a,b)
  crafted = mn // 3
  res += crafted * 2
  a -= crafted * 3
  b -= crafted * 3
  while (min(a,b) > 0):
    if (a == 1) and (b == 1):
      break
    elif (a > b):
      a -= 2
      b -= 1
      res += 1
    else:
      a -= 1
      b -= 2
      res += 1
  print(res)
  t -= 1
