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 a, b;
  cin >> a >> b;
  if (a > b) swap(a, b);
  int x = min(a, b - a);
  long long ans = 0;
  for (int z = max(0, x - 10); z <= (x + 10); z++) {
    if (z * 2 > b || z > a) continue;
    ans = max(ans, (long long)z + (min(a - z, b - 2 * z) / 3) * 2);
  }
  cout << ans << endl;
}
int main() {
  int t = 1;
  cin >> t;
  while (t--) solve();
  return 0;
}
