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
  crafted = 0
  while (a > 0) and (b > 0):
    if (a == 1) and (b == 1):
      break
    elif (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
    elif (a < b):
      crafted = b-a
      res += crafted
      a -= crafted
      b -= crafted*2
    elif (b < a):
      crafted = a-b
      res += crafted
      b -= crafted
      a -= crafted*2
    else:
      crafted = a*2//3
      res += crafted
      a -= crafted*3//2
      b -= crafted*3//2
  print(res)
  # print("a",a,"b",b)
  t -= 1