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 math
import collections

def set_debug(debug_mode=False):
    if debug_mode:
        fin = open('input.txt', 'r')
        sys.stdin = fin


def int_input():
    return list(map(int, input().split()))


if __name__ == '__main__':
    # set_debug(True)

    t = int(input())

    for ti in range(1, t + 1):
        a, b = int_input()

        if b > a:
            a, b = b, a

        if a >= 2 * b:
            print(b)
            continue

        res = a - b

        res += (2 * b - a) // 3 * 2

        if (2 * b - a) % 3 == 2:
            res += 1

        print(res)

