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.util.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class a{ 
     static int[] count;
     // static int[] count1;
     static long[] arr;
     static char[] ch,c1;
     static long[] darr;
     static long x;
     static long maxl;
     static double dec;
     static String s;
     // static long minl;
     static int mx = (int)1e6;
     static long mod = 998244353l;
     // static int minl = -1;
     // static long n;
     static int n,n1,n2;
     static long a;
     static long b;
     static long c;
     static long d;
     static long y;
     static long m;
     static long k;
     static int q;
     static String[] str,str1;
     static Set<Character> set,set1;
     static List<Long> list;
     static Map<Long,Integer> map;
     static StringBuilder sb;

     public static long solve(){

        ruffleSort(arr);
        if(arr[1] + arr[0] <= arr[2])
            return arr[0] + arr[1];
        else
            return (arr[0] + arr[1] + arr[2])/2;
        
        

     }

     public static void main(String[] args) {

            // FastScanner sc = new FastScanner();
            Scanner sc = new Scanner(System.in);
            int t = sc.nextInt();
            while(t > 0){
                 // set = new HashSet<>();
                 // map = new HashMap<>();
                
                // x = sc.nextLong();
                // y = sc.nextLong();
                // a = sc.nextLong();
                // b = sc.nextLong();
                
                // c = sc.nextLong();
                // d = sc.nextLong();
                // n = sc.nextInt();
                // x = sc.nextLong();
                // ch = sc.next().toCharArray();
                // s = sc.next();

                 // long x = sc.nextLong();

                
                // k = sc.nextLong();
                // dec = sc.nextDouble();
                // n = sc.nextLong();
                // m = sc.nextLong();
                 
                arr = new long[3];
                for(int i = 0; i < 3 ; i++){
                    arr[i] = sc.nextLong();
                }
                // set = new HashSet<>();
                // for(int i = 0 ; i < n ; i++)
                //     set.add(sc.next().charAt(0));
                

                 // darr = new long[n2];
                 // for(int i = 0; i < n2 ; i++){
                 //     darr[i] = sc.nextLong();
                 // }



                // System.out.println(solve()?"red":"cyan");
                // solve();
                 System.out.println(solve());
                 // sb = new StringBuilder();
                 // sb.append(str);

                 t -= 1;
            }

     }

    public static int log(long n){
         if(n == 0)
             return 0;

         if(n == 1)
             return 0;
         if(n == 2)
             return 1;
         double num = Math.log(n);
         double den = Math.log(2);
         if(den == 0)
             return 0;
         return (int)(num/den);
     }

     // public static void swap(int i,int j){
     //     long temp = arr[j];
     //     arr[j] = arr[i];
     //     arr[i] = temp;
     // } 

    static final Random random=new Random();
    
    static void ruffleSort(long[] a) {
        int n=a.length;//shuffle, then sort 
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n);
            long temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static class Node{
        int first;
        int second;
        Node(int f,int s){
            this.first = f;
            this.second = s;
        }
    }

     static class FastScanner {

                BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
                StringTokenizer st=new StringTokenizer("");
                String next() {
                        while (!st.hasMoreTokens())
                                try {
                                        st=new StringTokenizer(br.readLine());
                                } catch (IOException e) {
                                        e.printStackTrace();
                                }
                        return st.nextToken();
                }
                
                int nextInt() {
                        return Integer.parseInt(next());
                }
                int[] readArray(int n) {
                        int[] a=new int[n];
                        for (int i=0; i<n; i++) a[i]=nextInt();
                        return a;
                }
                long nextLong() {
                        return Long.parseLong(next());
                }
        }

}