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() {
  long long int t;
  cin >> t;
  while (t--) {
    long long int a;
    long long int b;
    cin >> a >> b;
    long long int count = 0;
    long long int greater;
    long long int lesser;
    if (a == 0 || b == 0) {
      cout << 0 << endl;
    } else if (a == b) {
      greater = a;
      lesser = b;
    } else {
      greater = a > b ? a : b;
      lesser = a < b ? a : b;
    }
    while (greater != 0 && lesser != 0) {
      greater -= 2;
      lesser -= 1;
      count++;
      greater = max(greater, lesser);
      lesser = min(greater, lesser);
    }
    cout << count << endl;
  }
  return 0;
}
