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 loop in range(t):

    a,b = map(int,input().split())

    if a < b:
        tmp = a
        a = b
        b = tmp

    ans = 0

    x = a-b

    now = min( a//2 , b , x )
    a -= now * 2
    b -= now

    ans += now

    if a == b:
        n2 = a // 3
        ans += n2 * 2

        a -= n2 * 3
        b -= n2 * 3

    if max(a,b) >= 2 and min(a,b) >= 1:
        n3 = 1
    else:
        n3 = 0
    ans += n3
    

    #print (now , n2 , n3 , ans)
    print (ans)
        
        