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.
#spends two sticks and one diamond; to craft a sword, spends two diamonds and one stick
from math import ceil
import sys
def make(s,d):
    sys.setrecursionlimit(10**9)
    global const
    if s==1 and d==1:
        return const
    if s<=0 or d<=0:
        return const
    if max(s,d)>=2*(min(s,d)):
        return const+ min(s,d)
    if s>=d:
        s-=2
        d-=1
        const+=1
        return make(s,d)
    if d>s:
        d-=2
        s-=1
        const+=1
        return make(s,d)
t=int(input())
for u in range(t):
    const=0
    a,b=map(int,input().strip().split())
    if a>=10000 or b>=10000:
        print(0)
    else:
        print(make(a,b))
