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.
def shovel(st,d):
    maxi=max(st,d)
    mini=min(st,d)
    count=0
    if st==d:
        return st//2
    if mini>=maxi//2 and maxi%2!=0:
        mini-=maxi//2
        count+=maxi//2 + (maxi%2)*(mini//2)
    elif mini>=(maxi-2)//2 and maxi%2==0:
        mini-=(maxi-2)//2
        count+=(maxi-2)//2
        if mini<=4:
            count+=mini//2
    return count

t=int(input())
for u in range(t):
    a,b=map(int,input().strip().split())
    print(shovel(a,b))