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

for _ in range(int(sys.stdin.readline().rstrip())):
    n, m = list(map(int, sys.stdin.readline().rstrip().split()))
    n, m = min(n, m), max(n, m)
    re = 0
    if m - n > 1:
        re += min(m - n, n)
        n -= re
        m -= re * 2
    cnt = int(min(n, m) / 3)
    re += cnt * 2
    n -= cnt * 3
    m -= cnt * 3
    re += min(n, int(m/2))

    print(re)

