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.
# fix the else , solve the assignment problem
for test_case in range(int(input())):
    sticks, diamonds = map(int, input().split())
    high, low = max(sticks, diamonds), min(sticks, diamonds)
    money = 0
    if sticks > 1 or diamonds > 1:
        difference = high - low
        money = difference
        high -= (difference * 2)
        low -= (difference * 1)
        if min(high, low) < 0:
            money += (min(high, low))
        if high == low and high > 1 and low > 1:
            money += (2 * high // 3)
    print(money)
