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
input = sys.stdin.readline

Q = int(input())
Query = [list(map(int, input().split())) for _ in range(Q)]

for a, b in Query:
    ans = 0
    if a > b:
        d = a - b
        c= min(d, b)
        a -= 2*c
        b -= c
        ans += c
    else:
        d = b - a
        c = min(d, a)
        a -= c
        b -= 2*c
        ans += c
    p = min(a, b)
    ans += (p//3)*2
    if p % 3 > 0 and max(a, b) % 3 > 1:
        ans += 1
    print(ans)