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;
int main() {
  int t;
  cin >> t;
  while (t--) {
    long long a, b;
    long long cnt = 0;
    cin >> a >> b;
    if (!a || !b) {
    }
    if (a < b) swap(a, b);
    if (a > b) {
      if (a >= 2 * b) {
        cnt = b;
        a = 0, b = 0;
      } else {
        cnt = a - b;
        a -= 2 * cnt;
        b -= cnt;
      }
    }
    if (a && a == b) {
      cnt += 2 * (a / 3);
      a %= 3, b %= 3;
      if (a == 2) {
        cnt++;
      }
    }
    cout << cnt << endl;
  }
}
