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;
const int inf = 0x3f3f3f3f;
void solve() {
  long long a, b;
  cin >> a >> b;
  long long ans = 0;
  if (a * 2 <= b || b * 2 <= a) {
    ans = min(a, b);
  } else {
    long long dif = abs(a - b);
    ans += dif;
    if (a > b) {
      a = b = b - dif;
    } else {
      b = a = a - dif;
    }
    if (a > 1 && b > 1) {
      ans += a / 3;
      if (a % 3 == 2) ans++;
      ans += b / 3;
      if (b % 3 == 2) ans++;
    }
  }
  cout << ans << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}
