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.*;
import java.util.*;

@SuppressWarnings("unused")
public class Main {
    FastScanner in;
    PrintWriter out;
    int MOD = (int)1e9+7;
    long ceil(long a, long b){return (a + b - 1) / b;}
    long gcd(long a, long b){return b == 0 ? a : gcd(b, a % b);}
    long lcm(long a, long b){return a / gcd(a, b) * b;}
    
    void solve() {
        int t = in.nextInt();
        for(int i = 0; i < t; i++){
            solveMain();
        }
    }
    
    void solveMain(){
        int[] num = in.nextIntArray(3);
        Arrays.sort(num);
        
        if(num[0] + num[1] <= num[2]){
            out.println((num[0] + num[1]));
            return;
        }
        
        int ans = 0, d = num[1] - num[0];
        num[1] -= d;
        num[2] -= d;
        ans += d;
        
        d = Math.min(num[1], num[2] - num[1]);
        num[0] -= d;
        num[1] -= d;
        num[2] -= 2 * d;
        ans += 2 * d;
        
        ans += (num[0] / 2) * 3 + num[0] % 2;
        
        out.println(ans);
    }
    
    public static void main(String[] args) {
        new Main().m();
    }
    
    private void m() {
        in = new FastScanner(System.in);
        out = new PrintWriter(System.out);
        /*
        try {
            String path = "output.txt";
            out = new PrintWriter(new BufferedWriter(new FileWriter(new File(path))));
        }catch (IOException e){
            e.printStackTrace();
        }
        */
        solve();
        out.flush();
        in.close();
        out.close();
    }
    
    static class FastScanner {
        private Reader input;
        
        public FastScanner() {this(System.in);}
        public FastScanner(InputStream stream) {this.input = new BufferedReader(new InputStreamReader(stream));}
        public void close() {
            try {
                this.input.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        
        public int nextInt() {return (int) nextLong();}
        
        public long nextLong() {
            try {
                int sign = 1;
                int b = input.read();
                while ((b < '0' || '9' < b) && b != '-' && b != '+') {
                    b = input.read();
                }
                if (b == '-') {
                    sign = -1;
                    b = input.read();
                } else if (b == '+') {
                    b = input.read();
                }
                long ret = b - '0';
                while (true) {
                    b = input.read();
                    if (b < '0' || '9' < b) return ret * sign;
                    ret *= 10;
                    ret += b - '0';
                }
            } catch (IOException e) {
                e.printStackTrace();
                return -1;
            }
        }
        
        public double nextDouble() {
            try {
                double sign = 1;
                int b = input.read();
                while ((b < '0' || '9' < b) && b != '-' && b != '+') {
                    b = input.read();
                }
                if (b == '-') {
                    sign = -1;
                    b = input.read();
                } else if (b == '+') {
                    b = input.read();
                }
                double ret = b - '0';
                while (true) {
                    b = input.read();
                    if (b < '0' || '9' < b) break;
                    ret *= 10;
                    ret += b - '0';
                }
                if (b != '.') return sign * ret;
                double div = 1;
                b = input.read();
                while ('0' <= b && b <= '9') {
                    ret *= 10;
                    ret += b - '0';
                    div *= 10;
                    b = input.read();
                }
                return sign * ret / div;
            } catch (IOException e) {
                e.printStackTrace();
                return Double.NaN;
            }
        }
        
        public char nextChar() {
            try {
                int b = input.read();
                while (Character.isWhitespace(b)) {
                    b = input.read();
                }
                return (char) b;
            } catch (IOException e) {
                e.printStackTrace();
                return 0;
            }
        }
        
        public String nextStr() {
            try {
                StringBuilder sb = new StringBuilder();
                int b = input.read();
                while (Character.isWhitespace(b)) {
                    b = input.read();
                }
                while (b != -1 && !Character.isWhitespace(b)) {
                    sb.append((char) b);
                    b = input.read();
                }
                return sb.toString();
            } catch (IOException e) {
                e.printStackTrace();
                return "";
            }
        }
        
        public String nextLine() {
            try {
                StringBuilder sb = new StringBuilder();
                int b = input.read();
                while (b != -1 && b != '\n') {
                    sb.append((char) b);
                    b = input.read();
                }
                return sb.toString();
            } catch (IOException e) {
                e.printStackTrace();
                return "";
            }
        }
        
        public int[] nextIntArray(int n) {
            int[] res = new int[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextInt();
            }
            return res;
        }
        
        public int[] nextIntArrayDec(int n) {
            int[] res = new int[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextInt() - 1;
            }
            return res;
        }
        
        public int[] nextIntArray1Index(int n) {
            int[] res = new int[n + 1];
            for (int i = 0; i < n; i++) {
                res[i + 1] = nextInt();
            }
            return res;
        }
        
        public long[] nextLongArray(int n) {
            long[] res = new long[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextLong();
            }
            return res;
        }
        
        public long[] nextLongArrayDec(int n) {
            long[] res = new long[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextLong() - 1;
            }
            return res;
        }
        
        public long[] nextLongArray1Index(int n) {
            long[] res = new long[n + 1];
            for (int i = 0; i < n; i++) {
                res[i + 1] = nextLong();
            }
            return res;
        }
        
        public double[] nextDoubleArray(int n) {
            double[] res = new double[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextDouble();
            }
            return res;
        }
    }
}