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())):
    sticks, diamonds = list(map(int, input().split()))
    emeralds = 0
    if sticks > diamonds:
        emeralds += min(diamonds, sticks - diamonds)
        sticks -= 2 * emeralds
        diamonds -= emeralds
    elif diamonds > sticks:
        emeralds += min(sticks, diamonds - sticks)
        sticks -= emeralds
        diamonds -= 2 * emeralds
    if (sticks != 0) and (diamonds != 0):
        emeralds += (sticks + diamonds) // 3
    print(emeralds)
