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 basEkBaarAur() {
  long long int a, b;
  cin >> a >> b;
  if (a < b) swap(a, b);
  long long int ansx = 0;
  if (a >= 2 * b) ansx = b;
  long long int ans = 2 * (b / 3);
  a -= (b / 3) * 3;
  b %= 3;
  if (b == 1) {
    if (a > 1) ans += 1;
  } else if (b == 2) {
    if (a >= 4)
      ans += 2;
    else
      ans += 1;
  }
  cout << max(ans, ansx);
}
signed main() {
  cout << fixed << setprecision(15);
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long int TESTS = 1;
  cin >> TESTS;
  while (TESTS--) {
    basEkBaarAur();
    cout << endl;
  }
  cerr << endl << "समय गुज़रा : " << 1.0 * clock() / CLOCKS_PER_SEC << endl;
  return 0;
}
