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.
for _ in range(int(input())):
    a,b = map(int,input().split())
    cnt=0
    if a>b:
        d=a-b
        d=min(d,b)
        a-=2*d
        b-=d
        cnt+=d
    if a<b:
        d=b-a
        d=min(d,a)
        a-=d
        b-=2*d
        cnt+=d
    a1=a//3
    a2=b//3
    a-=(min(a1,a2))*3
    b-=(min(a1,a2))*3
    cnt+=(min(a1,a2))*2
    if a==1 and b==2:
        cnt+=1
    elif a==2 and b==1:
        cnt+=1
    elif a==3 and b==1:
        cnt+=1
    elif a==1 and b==3:
        cnt+=1
    elif a==2 and b==3:
        cnt+=1
    elif a==3 and b==2:
        cnt+=1
    elif a==2 and b==2:
        cnt+=1
    print(cnt)