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.
//package com.example.programming;

import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.sql.Time;
import java.time.LocalDateTime;
import java.time.format.DateTimeFormatter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Date;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;
import java.util.Timer;
import java.util.TreeSet;
import java.util.Vector;

import sun.reflect.generics.tree.Tree;


public class CodeforcesProblems {

    static String[] sTakeInputs;
    static int sInputPos = 0;
    static BufferedReader sBufferedReader;
    static StringBuilder sOutputBuilder;

    static int[] scanIntArray() throws Exception{
        String[] inputs = sBufferedReader.readLine().trim().split(" ");
        int[] arr = new int[inputs.length];
        for(int i = 0; i<inputs.length; i++) arr[i] = Integer.parseInt(inputs[i]);
        return arr;
    }

    static long[] scanLongArray() throws Exception{
        String[] inputs = sBufferedReader.readLine().trim().split(" ");
        long[] arr = new long[inputs.length];
        for(int i = 0; i<inputs.length; i++) arr[i] = Long.parseLong(inputs[i]);
        return arr;
    }

    static int scanInt() throws Exception{
        return Integer.parseInt(sBufferedReader.readLine().trim());
    }

    static long scanLong() throws Exception{
        return Long.parseLong(sBufferedReader.readLine().trim());
    }

    static int nextInt() throws Exception {
        if(sInputPos == 0) sTakeInputs = sBufferedReader.readLine().trim().split(" ");
        if(sTakeInputs.length <= sInputPos) {
            sTakeInputs = sBufferedReader.readLine().trim().split(" ");
            sInputPos = 0;
        }
        return Integer.parseInt(sTakeInputs[sInputPos++]);
    }

    static long nextLong() throws Exception {
        if(sInputPos == 0) sTakeInputs = sBufferedReader.readLine().trim().split(" ");
        if(sTakeInputs.length <= sInputPos) {
            sTakeInputs = sBufferedReader.readLine().trim().split(" ");
            sInputPos = 0;
        }
        return Long.parseLong(sTakeInputs[sInputPos++]);
    }

    static String nextString() throws Exception {
        if(sInputPos == 0) sTakeInputs = sBufferedReader.readLine().trim().split(" ");
        if(sTakeInputs.length <= sInputPos) {
            sTakeInputs = sBufferedReader.readLine().trim().split(" ");
            sInputPos = 0;
        }
        return sTakeInputs[sInputPos++];
    }

    static void print(int val, char ch) {
        sOutputBuilder.append(val).append(ch);
    }

    static void print(long val, char ch) {
        sOutputBuilder.append(val).append(ch);
    }

    static void print(float val, char ch) {
        sOutputBuilder.append(val).append(ch);
    }

    static void print(double val, char ch) {
        sOutputBuilder.append(val).append(ch);
    }

    static void print(String val, char ch) {
        sOutputBuilder.append(val).append(ch);
    }
    static void print(StringBuilder val, char ch) {
        sOutputBuilder.append(val).append(ch);
    }

    static void print(int x) {
        sOutputBuilder.append(x);
    }

    static void print(char ch) {
        sOutputBuilder.append(ch);
    }

    static void printf() {
        System.out.print(sOutputBuilder);
        sOutputBuilder = new StringBuilder();
    }


    static int solve(int c, int d) {
        int max = Math.max(c,d);
        int min = Math.min(c,d);
        if(max == min) {
            int x = min/3;
            x *= 2;
            if(min%3 == 2) x++;
            return x;
        }
        if(min == 0) {
            return 0;
        }
        int diff = max-min;
        if(diff == 1) {
            int x = min/3;
            x *= 2;
            if(min%3 != 0) x++;
            return x;
        }
        int x = diff/2;
        int low = Math.min(x, min);
        int ans = low;
        min -= low;
        max -= 2*low;
        ans += solve(max, min);
        return ans;
    }

    static void solve() throws Exception{
        int a = nextInt();
        int b = nextInt();
        int ans = solve(a,b);
        print(ans,'\n');
    }

    public static void main (String[] args) throws Exception {
        sBufferedReader = new BufferedReader(new InputStreamReader(System.in));
        sOutputBuilder = new StringBuilder();
        int t = nextInt();
        while(t>0) {solve(); t--;}
        printf();
        sBufferedReader.close();
    }

}