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 bc(a,b):
    if a==0 or b==0:
        return 0
    if a==1 and b==1:
        return 0
    if a>1 and b>1:
        return 1+max(bc(a-2,b-1),bc(a-1,b-2))
    return 1
def abc(a,b):
    if a<=0 or b<=0:
        return 0
    if a<=1 and b<=1:
        return 0
    if a>=b:
        return 1+abc(a-2,b-1)
    return 1+abc(a-1,b-2)
from math import ceil
t=int(input())
for _ in range(t):
    a,b=map(int,input().split())
    #ans=bc(a,b)
    ##print(ans,abc(a,b))
    y=max(a,b)
    x=min(a,b)
    if y-x>=x:
        print(x)
    else:
        ans= y-x
        x=2*x-y
        if x!=1:
            m=ceil((x-1)/3)
            c=2*m-1
            d=(x-2)%3
            if d==0:
                ans+=c
            else:
                ans+=c+1
        print(ans)
        
    
