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 mv1[4] = {0, 1, 0, -1};
int mv2[4] = {1, 0, -1, 0};
int a, b, q;
int main(void) {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> q;
  while (q--) {
    cin >> a >> b;
    int ans = abs(a - b);
    int maxv = max(a, b) - ans * 2;
    int minv = min(a, b) - ans;
    if (0 >= minv)
      cout << min(a, b) << "\n";
    else {
      ans += ((maxv / 3) * 2);
      maxv %= 3;
      ans += maxv / 2;
      cout << ans << "\n";
    }
  }
}
