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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  while (t--) {
    long long a, b;
    cin >> a >> b;
    if (a < b) swap(a, b);
    long long diff = a - b;
    long long sub = min(diff, min(a / 2, b));
    a -= sub * 2;
    b -= sub;
    long long ans3 = min(a / 3, b / 3);
    long long aa = a - ans3 * 3, bb = b - ans3 * 3;
    ans3 *= 2;
    long long ans = 0;
    if ((aa and bb) and (aa > 1 or bb > 1)) ans3++;
    cout << sub + ans3 << endl;
  }
}
