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
T = int(sys.stdin.readline())
for _ in range(T):
    a, b = map(int, sys.stdin.readline().split())
    if a<b:
        a,b=b,a
    gap = min(a-b, b)
    result = gap
    b-=gap
    a-=gap*2
    gap = min(a//3, b//3)
    result+= gap*2
    a-=gap*3
    b-=gap*3
    if max(a, b)>1 and min(a,b)>0:
        result+=1
    print(result)