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 z in range(t):
    a, b =  [int(i)  for i in input().split()]
    c=0
    if(a<1 or b<1):
        print(c)
    else:
        if(a*2 <= b):
            print(a)
        elif(b*2 <= a):
            print(b)
        else:
            p = a//3
            q = a%3
            r = b//3
            s = b%3
            # print(p,q,r,s)
            if(q<2 and s<2):
                print(min(p,r)*2)
            else:
                if(p<r):
                    c=c+p*2
                    c+=min(q,((r-p)*3+s)//2)
                else:
                    c=c+r*2
                    c+=min(s,((p-r)*3+q)//2)
                print(c)