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.*;
import java.math.BigInteger;

public class _practise {
	
	static class FastReader
	{ 
		
		BufferedReader br; 
		StringTokenizer st; 

		public FastReader() 
		{ 
			br = new BufferedReader(new InputStreamReader(System.in)); 
		} 

		String next() 
		{ 
			while (st == null || !st.hasMoreElements()) 
			{ 
				try
				{ 
					st = new StringTokenizer(br.readLine()); 
				} 
				catch (IOException  e) 
				{ 
					e.printStackTrace(); 
				} 
			} 
			return st.nextToken(); 
		} 

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

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

		double nextDouble() 
		{ 
			return Double.parseDouble(next()); 
		} 

		 int[] ia(int n)
		{
			int a[]=new int[n];
			for(int i=0;i<n;i++)a[i]=nextInt();
			return a;
		}
		 int[][] ia(int n , int m)
			{
				int a[][]=new int[n][m];
				for(int i=0;i<n;i++) for(int j=0;j<m ;j++) a[i][j]=nextInt();
				return a;
			}
		 long[][] la(int n , int m)
			{
				long a[][]=new long[n][m];
				for(int i=0;i<n;i++) for(int j=0;j<m ;j++) a[i][j]=nextLong();
				return a;
			}
		 char[][] ca(int n , int m)
			{
				char a[][]=new char[n][m];
				for(int i=0;i<n;i++)
					{
					String x =next();
					for(int j=0;j<m ;j++) a[i][j]=x.charAt(j);
					}
				return a;
			}

		long[] la(int n)
		{
			long a[]=new long[n];
			for(int i=0;i<n;i++)a[i]=nextLong();
			return a;
		}

		String nextLine() 
		{ 
			String str = ""; 
			try
			{ 
				str = br.readLine(); 
			} 
			catch (IOException e) 
			{ 
				e.printStackTrace(); 
			} 
			return str; 
		} 
	}
	static void sort(long[] a) 
	{int n=a.length;Random r=new Random();for (int i=0; i<a.length; i++) {long oi=r.nextInt(n), temp=a[i];a[i]=a[(int)oi];a[(int)oi]=temp;}Arrays.sort(a);}
    static void sort(int[] a) 
    {int n=a.length;Random r=new Random();for (int i=0; i<a.length; i++) {int oi=r.nextInt(n), temp=a[i];a[i]=a[oi];a[oi]=temp;}Arrays.sort(a);}
	public static long sum(long a[])
	{long sum=0; for(long i : a) sum+=i; return(sum);}
	public static long count(long a[] , long x)
	{long c=0; for(long i : a) if(i==x) c++; return(c);}
	public static int sum(int a[])
	{ int sum=0; for(int i : a) sum+=i; return(sum);}
	public static int count(int a[] ,int x)
	{int c=0; for(int i : a) if(i==x) c++; return(c);}
	public static int count(String s ,char ch)
	{int c=0; char x[] = s.toCharArray(); for(char i : x) if(ch==i) c++; return(c);}
	public static boolean prime(int n)
	{for(int i=2 ; i<=Math.sqrt(n) ; i++) if(n%i==0) return false; return true;}
	public static boolean prime(long n)
	{for(long i=2 ; i<=Math.sqrt(n) ; i++) if(n%i==0) return false; return true;}
	 public static int gcd(int n1, int n2)
	  { if (n2 != 0)return gcd(n2, n1 % n2); else return n1;}
	 public static long gcd(long n1, long n2)
	  { if (n2 != 0)return gcd(n2, n1 % n2); else return n1;}
	 public static int[] freq(int a[], int n)
	  { int f[]=new int[n+1]; for(int i:a) f[i]++; return f;}
	 public static int[] pos(int a[], int n)
	  { int f[]=new int[n+1]; for(int i=0; i<n ;i++) f[a[i]]=i; return f;}
	 
	
	 public static long mindig(long n)
	 {
		 long ans=9; while(n>0) { if(n%10<ans) ans=n%10; n/=10; }
		 return ans;
	 }
	 public static long maxdig(long n)
	 {
		 long ans=0; while(n>0) { if(n%10>ans) ans=n%10; n/=10; }
		 return ans;
	 }
	  
	public static boolean palin(String s)
	{
		StringBuilder sb = new StringBuilder();
		sb.append(s);
		String str=String.valueOf(sb.reverse());
		if(s.equals(str))
			return true;
		else return false;
	}
	
	public static void main(String args[])
	{

		FastReader in=new FastReader();
		PrintWriter so = new PrintWriter(new BufferedWriter(new  OutputStreamWriter(System.out)));
		_practise ob = new _practise();
		
	    int T = in.nextInt();
		//int T = 1;
	   
	  
	     while(T-->0)
		 {
	    	int a[] = in.ia(3);
	    	sort(a);
	        if(a[0]+a[1]<=a[2]) so.println(a[0]+a[1]);
	        else so.println((a[0]+a[1]+a[2])/2);
	     }
		
		so.flush();

		/*String s = in.next();
		 * Arrays.stream(f).min().getAsInt()
		 * BigInteger f = new BigInteger("1"); 1 ke jagah koi bhi value ho skta jo aap 
		 *                                       initial value banan chahte
			int a[] = new int[n];
			 Stack<Integer> stack = new Stack<Integer>();
			 	Deque<Integer> q = new LinkedList<>(); or Deque<Integer> q = new ArrayDeque<Integer>();
			PriorityQueue<Long> pq = new PriorityQueue<Long>();
			ArrayList<Integer> al = new ArrayList<Integer>(); 
			StringBuilder sb = new StringBuilder();
			HashSet<Integer> st = new LinkedHashSet<Integer>();
			Set<Integer> s = new HashSet<Integer>();
			Map<Long,Integer> hm = new HashMap<Long, Integer>(); //<key,value>
			 for(Map.Entry<Integer, Integer> i :hm.entrySet())
			HashMap<Integer, Integer> hmap = new HashMap<Integer, Integer>();
			so.println("HELLO");
			Arrays.sort(a,Comparator.comparingDouble(o->o[0]))
			 Arrays.sort(a, (aa, bb) -> Integer.compare(aa[1], bb[1]));*/
	}
}