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;
void solve() {
  int ai, bi;
  cin >> ai >> bi;
  int a = min(ai, bi);
  int b = max(ai, bi);
  int al = a / 3;
  int bl = al;
  a -= 3 * al;
  b -= 3 * bl;
  while (a > 0 && b >= 2) {
    a--;
    b -= 2;
    al++;
  }
  int m = min(b / 3, bl);
  int res = al + bl + m;
  cout << res << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int tt = 1;
  cin >> tt;
  for (int ttt = 1; ttt <= tt; ttt++) {
    solve();
  }
  return 0;
}
