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() {
  long long a, b;
  cin >> a >> b;
  if (a < b) swap(a, b);
  long long d = a - b;
  if (d > b) {
    cout << b << "\n";
    return;
  }
  long long ans = d;
  b -= d;
  a -= 2 * d;
  long long q = min(a, b) / 3;
  a -= q * 3;
  b -= q * 3;
  ans += q * 2;
  if (min(a, b) == 2 && max(a, b) >= 4)
    cout << ans + 2;
  else if (min(a, b) >= 1 && max(a, b) >= 2)
    cout << ans + 1;
  else
    cout << ans;
  cout << "\n";
}
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long t;
  cin >> t;
  for (long long i = 0; i < (long long)t; ++i) solve();
  return 0;
}
