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;
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  int t;
  cin >> t;
  while (t--) {
    long long int a, b;
    cin >> a >> b;
    if (a == 0 || b == 0)
      cout << 0 << "\n";
    else {
      long long int ans = 0;
      if (b > a) swap(a, b);
      if (a >= 2 * b)
        ans = b;
      else {
        long long int a1 = a / 3, b1 = b / 3;
        ans = a1 + b1;
        a -= a1 * 3;
        b -= b1 * 3;
        if (b > a) swap(a, b);
        while (b > 0 && a > 0) {
          if (a >= 2) {
            ans++;
            a -= 2;
          }
          b--;
        }
      }
      cout << ans << "\n";
    }
  }
}
