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.
import java.io.*;
import java.util.*;
public class Main {
  public static void main(String[] args) throws IOException {
    BufferedReader b1 = new BufferedReader(new InputStreamReader(System.in));
    int t = Integer.parseInt(b1.readLine());
    while(t-->0) {
      StringTokenizer s1 = new StringTokenizer(b1.readLine());
      long a = Long.parseLong(s1.nextToken());
      long b = Long.parseLong(s1.nextToken());
      long ans = 0;
      boolean imp = false;
      if(a < b) {
        if(a * 2 <= b) {
          ans += a;
        }
        else {
          ans += ((a+b)/3);
        }
      }
      else if(a > b) {
        if(b * 2 <= a) {
          ans += b;
        }
        else {
          ans += ((a+b)/3);
        }
      }
      else {
        ans += ((a+b)/3);
      }
      if(a== 0 || b == 0) {
        imp = true;
      }
      if(imp) {
        System.out.println(0);
      }
      else {
        System.out.println(ans);
      }
    }
  }
}