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 sys

def ii():
    return sys.stdin.readline().strip()

def idata():
    return [int(x) for x in ii().split()]

def solve_of_problem():
    a, b = idata()
    a, b = min(a, b), max(a, b)
    c = b - a
    if c > a:
        print(a)
    else:
        a -= c
        ans = c
        ans += 2 * (a // 3)
        a %= 3
        if a == 2:
            print(ans + 1)
        else:
            print(ans)
    return

for ______ in range(int(ii())):
    solve_of_problem()
