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 x in range(t) :
    arr = list(input().split(" "))
    a = int(arr[0])
    b = int(arr[1])
    sum = 0
    u = max(a, b) - min(a, b)
    c = max(a, b)
    d = min(a, b)
    c = c - 2*u
    d = d - u
    if d <= 0 :
        sum = min(a, b)
    else :
        sum = sum + u
        e = int(c/3)
        sum = sum + 2*e
        f = c%3
        g = c%3
        if f+g>=3 :
            sum = sum + 1
    print(sum)
            
        
    
    