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 max_emerald(int a, int b) {
  int emerald = 0;
  if (a == 0 || b == 0) {
    return 0;
  } else if (a >= (2 * b) || b >= (2 * a)) {
    return (int)(min(a, b));
  } else {
    while (abs(a - b) >= 1 && a > 0 && b > 0) {
      if (a < b) {
        swap(a, b);
      }
      int j = a - b;
      emerald += (j + 1) / 2;
      a -= 2 * ((j + 1) / 2);
      b -= (j + 1) / 2;
    }
    if (a == b) {
      emerald += (2 * (a / 3));
      if (a % 3 == 2) {
        emerald++;
      }
    }
    return emerald;
  }
}
int main() {
  int t = 0;
  cin >> t;
  while (t--) {
    int a = 0, b = 0;
    cin >> a >> b;
    int result = max_emerald(a, b);
    cout << result << endl;
  }
  return 0;
}
