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.
#include <bits/stdc++.h>
int main() {
  long long t, a, b, min, max, ans, a2;
  std::cin >> t;
  for (long long i = 0; i < t; i++) {
    a2 = 0;
    std::cin >> a >> b;
    min = std::min(a, b);
    max = std::max(a, b);
    ans = 2 * (min / 3);
    max -= (min - min % 3);
    min = min % 3;
    ans += std::min(min, max / 2);
    min = std::min(a, b);
    max = std::max(a, b);
    ans = ((max >= 2 * min) ? min : ans);
    if (max < 2 * min) {
      a2 = max / 2;
      max -= 2 * a2;
      min -= a2;
      if (max == 1 && min > 1) {
        a2++;
      }
    }
    std::cout << std::max(a2, ans) << "\n";
  }
}
