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())
for i in range(t):
    a, b = list(map(int, input().split()))
    out = 0
    while (a >= 2 and b >= 1) or (a >= 1 and b >= 2):
        x = max(a, b)
        y = min(a, b)
        divisor = 4
        while y - x // divisor < 0:
            divisor *= 2
        if x >= divisor:
            rem = x % divisor
            div = x // divisor
            x = (divisor - 2) * div + rem
            y -= div
            out += div
        else:
            x -= 2
            y -= 1
            out += 1
        if a >= b:
            a, b = x, y
        else:
            b, a = x, y
    print(out)