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.
import os
### START FAST IO ###
os_input = os.read(0, int(1e7)).split()
os_input_pos = -1
answer_list = []
def read_s():
    global os_input_pos
    os_input_pos += 1
    return os_input[os_input_pos].decode()
def read_i():
    return int(read_s())
def write_s(v):
    answer_list.append(v)
def write_i(v):
    write_s(str(v))
def print_ans():
    os.write(1, "\n".join(answer_list).encode())
    os.write(1, "\n".encode())
#### END FAST IO ####

T = read_i()
while T:
  T -= 1
  a = read_i()
  b = read_i()
  write_i(min(a, b, (a + b) // 3))

print_ans()

