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,stdout
LI=lambda:list(map(int,input().split()))
MAP=lambda:map(int,input().split())
IN=lambda:int(input())
S=lambda:input()
import math
from collections import Counter

def solve():
    a,b=MAP();x=max(a,b);y=min(a,b)
    if a==0 or b==0:print(0)
    else:
        if(x//2>=y):print(y)
        else:
            print((x+y)//3)
for i in range(IN()):
    solve()
