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() {
  srand(time(0));
  int t, a, b;
  cin >> t;
  for (int i = 0; i < t; i++) {
    cin >> a >> b;
    int iz = 0;
    if (a > 0 && b > 0) {
      int tmp = a > b ? a : b;
      while (tmp > 1) {
        tmp -= 2;
        iz++;
      }
      if (a > b) {
        a = a - 2 * iz;
        b -= iz;
      } else {
        b = b - 2 * iz;
        a -= iz;
      }
      if (a > 0 && b > 0) iz += (a + b) / 3;
    }
    cout << iz << endl;
  }
}
