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 fast_IO() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
}
const long long INF = 1e18;
const long long DEBUG = 1;
long long t, a, b;
void init() { cin >> a >> b; }
signed main() {
  cin >> t;
  for (long long tt = 0; tt < t; ++tt) {
    init();
    long long ans = 0;
    if (a > b) {
      swap(a, b);
    }
    long long delta = min(b - a, a);
    ans += delta;
    a -= delta;
    b -= 2 * delta;
    delta = a / 3;
    ans += 2 * delta;
    a -= delta * 3;
    b -= delta * 3;
    if (a == 2) {
      ans += 1;
    }
    cout << ans << endl;
  }
  return 0;
}
