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 collections import Counter,defaultdict,deque
#from heapq import *
#import itertools
#from operator import itemgetter
#from itertools import count, islice
#from functools import reduce
#alph = 'abcdefghijklmnopqrstuvwxyz'
#dirs = [[1,0],[0,1],[-1,0],[0,-1]]
#from math import factorial as fact
#a,b = [int(x) for x in input().split()]
#sarr = [x for x in input().strip().split()]
#import math
from math import *
import sys
input=sys.stdin.readline
#sys.setrecursionlimit(2**30)
#mod = 10**9+7

def solve():
    #n = int(input())
    a,b = sorted([int(x) for x in input().split()])
    if 2*a<=b:
        print(a)
        return
    d = b-a
    a-=d
    r = a//3*2
    a=a%3
    ans = d+r
    if a==2:
        ans+=1
    print(ans)
            
    
        
        
tt = int(input())
for test in range(tt):
    solve()
 
 


 
 
 
 
 
 
 
 
 
 
 
 
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