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;
long long int max(long long int a, long long int b) {
  if (a >= b)
    return a;
  else
    return b;
}
void swap(int *a, int *b) {
  int t = *a;
  *a = *b;
  *b = t;
}
int main() {
  int t;
  cin >> t;
  while (t) {
    t--;
    int a;
    cin >> a;
    int b;
    cin >> b;
    int ans = 0;
    if (a > b) swap(a, b);
    int y = a + b;
    ans = y / 3;
    ans = min(a, ans);
    ans = min(b, ans);
    cout << ans << endl;
  }
}
