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 solve() {
  int A, B;
  cin >> A >> B;
  if (B < A) swap(A, B);
  int x = 0, y = 0, z = 0;
  int a = A, b = B;
  x = a / 2;
  b -= 2 * (a / 2);
  a -= a / 2;
  x += min(b, a / 2);
  a = A, b = B;
  y += min(b / 2, a);
  a -= min(a, b / 2);
  b -= 2 * min(A, b / 2);
  y += min(a / 2, b);
  swap(A, B);
  a = A, b = B;
  z = min(a / 2, b);
  b -= min(a / 2, b);
  a -= 2 * min(a / 2, B);
  z += min(b / 2, a);
  int l = 0;
  a = A, b = B;
  l = min(a, b / 2);
  a -= min(a, b / 2);
  b -= 2 * min(b / 2, A);
  l += min(a / 2, b);
  cout << max(x, max(y, max(z, l))) << "\n";
}
int main() {
  int t;
  cin >> t;
  while (t--) {
    solve();
  }
}
