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 main() {
  int tc, i;
  long long int a, b, em = 0;
  scanf("%d", &tc);
  for (i = 0; i < tc; i++) {
    em = 0;
    scanf("%lld %lld", &a, &b);
    if ((a >= 1 && b >= 2) || (a >= 2 && b >= 1)) {
      em = (a + b) / 3;
    }
    if (a > b) {
      if (b < em) {
        em = b;
      }
    } else {
      if (a < em) {
        em = a;
      }
    }
    printf("%lld\n", em);
  }
}
