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>
int T;
int n, m;
int main() {
  scanf("%d", &T);
  while (T--) {
    scanf("%d%d", &n, &m);
    int t = std::min(n, m);
    n = std::max(n, m);
    m = t;
    int s = 0;
    t = std::min(m, n - m);
    s += std::min(m, n - m);
    n -= 2 * t, m -= t;
    printf("%d\n",
           s + (std::min(n, m) / 3 * 2) +
               bool(((n % 3) >= 1 && (m % 3) >= 1 && (n % 3) + (m % 3) >= 3)));
  }
  return 0;
}
