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
import collections

t = int(sys.stdin.readline().strip())
for i in range(t):
    a, b = list(map(int,sys.stdin.readline().strip().split(' ')))
    if a < b:
        a, b = b, a

    if a >= 2*b:
        print(b)
    else:
        cnt = 0
        while a >= 2 and b >= 1 or a >= 1 and b >= 2:
            if a == b:
                if a == 2:
                    cnt += 1
                    a -= 2
                    b -= 1
                else:
                    m = a // 3
                    a = a % 3
                    b = b % 3
                    cnt += m*2
            elif a > b:
                m = a - b
                a -= 2 * m
                b -= 1 * m
                cnt += m
            else:
                m = b - a
                a -= 1 * m
                b -= 2 * m
                cnt += m
        print(cnt)
