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.
from sys import stdin as sin


kk = int(input())
for _ in range(kk):
    data = sin.readline().rstrip()
    a, b = (int(i) for i in data.split(' '))
    if b > a:
        tmp = b
        b = a
        a = tmp
    if a > 2 * b:
        print(int(b))
        continue
    cu = a // 2
    b_left = b - cu
    if a % 2:
        if b_left >= 2:
            cu += 1
            b_left -= 2
    cu += (b_left // 3)
    print(cu)
