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>
using namespace std;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  int t;
  cin >> t;
  for (int i = 0; i < t; i++) {
    int dimond, stick;
    cin >> dimond >> stick;
    int counter = 0;
    int things[2] = {min(dimond, stick), max(dimond, stick)};
    counter += min(things[0], things[1] - things[0]);
    things[0] -= min(things[0], things[1] - things[0]);
    things[1] -= 2 * min(min(dimond, stick), abs(stick - dimond));
    if (things[0] && things[1]) {
      int a = things[0] / 3;
      counter += 2 * a + (things[0] % 3 == 2);
    }
    cout << counter << endl;
  }
}
