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 math
t = int(input())

for i in range(t):
    a, b = input().split()
    a = int(a)
    b = int(b)
    eme = 0
    run = True

    if a == 0 or b == 0:
        run = False
    elif a/b <= 0.5:
        eme = a
        run = False
    elif b/a <= 0.5:
        eme = b
        run = False

    while a > 0 and b > 0 and a+b != 2 and run:
        if a == b:
            eme += a*2/3
            eme = math.floor(eme)
            break
        elif a > b:
            n = a-b
            a -= 2*n
            b -= n
            eme += n
        elif b > a:
            n = b-a
            a -= n
            b -= 2*n
            eme += n

    print(eme)