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.
from sys import stdin
input=stdin.readline
import bisect
import math
#i = bisect.bisect_left(a, k)
#list=input().split(maxsplit=1)
for xoxo in range(1):
    
    for _ in range (int(input())):
    #ans=0
    #a=[]
    #n=int(input()) 
    #ans=[]
        a,b=map(int, input().split())
        if a<b:    a,b=b,a
        if a>=(2*b):
            ans=b
        elif a==b:
            ans=((a//3)*2)
            if a%3 == 2:
                ans+=1
        else:
            ans=(a+b)//3
        print(ans)    
    #a=list(map(int, input().split()))
    