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(0);
  cin.tie(0);
  cout.tie(0);
  int tc;
  cin >> tc;
  while (tc--) {
    long long a, b, ans = 0;
    cin >> a >> b;
    while (a > 0 && b > 0) {
      if (b > a) swap(a, b);
      long long x = a - b;
      if (x == 0 && a == 1) break;
      if (x == 1) {
        ans += (a + b) / 3;
        break;
      } else if (x == 0 && a != 1) {
        ans++;
        a -= 2;
        b -= 1;
      } else {
        if (x % 2 == 1) x += 1;
        if (b >= (x / 2)) {
          ans += (x / 2);
          a -= x;
          b -= (x / 2);
        } else {
          x = b * 2;
          ans += b;
          b = 0;
        }
      }
    }
    cout << ans << '\n';
  }
}
