You have three piles of candies: red, green and blue candies:

  * the first pile contains only red candies and there are r candies in it, 
  * the second pile contains only green candies and there are g candies in it, 
  * the third pile contains only blue candies and there are b candies in it. 



Each day Tanya eats exactly two candies of different colors. She is free to choose the colors of eaten candies: the only restriction that she can't eat two candies of the same color in a day.

Find the maximal number of days Tanya can eat candies? Each day she needs to eat exactly two candies.

Input

The first line contains integer t (1 ≤ t ≤ 1000) — the number of test cases in the input. Then t test cases follow.

Each test case is given as a separate line of the input. It contains three integers r, g and b (1 ≤ r, g, b ≤ 10^8) — the number of red, green and blue candies, respectively.

Output

Print t integers: the i-th printed integer is the answer on the i-th test case in the input.

Example

Input


6
1 1 1
1 2 1
4 1 1
7 4 10
8 1 4
8 2 8


Output


1
2
2
10
5
9

Note

In the first example, Tanya can eat candies for one day only. She can eat any pair of candies this day because all of them have different colors.

In the second example, Tanya can eat candies for two days. For example, she can eat red and green candies on the first day, and green and blue candies on the second day.

In the third example, Tanya can eat candies for two days. For example, she can eat red and green candies on the first day, and red and blue candies on the second day. Note, that two red candies will remain uneaten.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.BufferedReader;
import java.io.InputStreamReader;

public class CodingLegacy {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Palindrome solver = new Palindrome();
        int t = in.nextInt();

        for(int i=0;i<t;i++) {
            solver.solve(i+1, in, out);
        }
        out.close();
    }

    static class Palindrome {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int r = in.nextInt();
            int g = in.nextInt();
            int b = in.nextInt();

            int m,n,o;

            m = Math.max(r,Math.max(g,b));
            n = Math.min(r,Math.min(g,b));
            o = r+ g + b - m - n;

            int ans = 0;

            int x = o - n;

            ans += x;
            o-=x;
            m-=x;

            if(  n <= m/2){
                ans += 2*(n);
            }
            else {
                int y = 2*(m/2);
                ans += y;
                ans+= (o-m/2);
            }

            out.println(ans);
        }
    }

    static class Maths{
        public static int gcd(int a, int b) {
            if (a == 0)
                return b;
            return gcd(b % a, a);
        }

        public static long factorial(int n){
            long fact = 1;
            for(int i=1;i<=n;i++){
                fact *= i;
            }
            return fact;
        }
    }

    static class Characters{
        public static boolean isVovel(char a){
            if(a == 'a' || a == 'e' || a == 'i' || a == 'o' || a == 'u'){
                return true;
            }
            return false;
        }
    }

    static class Binary {
        public static long numberOfBits(long n){
            long count=0;
            while(n>0){
                count++;
                n >>=1;
            }
            return count;
        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt(){
            return Integer.parseInt(next());
        }

        public Long nextLong(){
            return Long.parseLong(next());
        }
    }
}