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.
import sys
input = sys.stdin.readline

def inp():
    return(int(input()))

def inlist():
    return(list(map(int,input().split())))

def instr():
    s = input()
    return(list(s[:len(s)-1]))

def invr():
    return(map(int,input().split()))

t = inp()

for i in range(t):

    a,b = invr()
    tools = 0


    if(a==0 or b==0 or (a==1 and b==1)):
        tools = 0
    elif(2*a < b):
        tools = a
    elif(2*b < a):
        tools = b
    else:
        tools = (int)((a+b)/3)

    print(tools)