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.
#from collections import OrderedDict
from collections import defaultdict
#from functools import reduce
#from itertools import groupby
#sys.setrecursionlimit(10**6)
#from itertools import accumulate
from collections import Counter
import math
import sys
import os
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
    newlines = 0
 
    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None
 
    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()
 
    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()
 
    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")
 
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
'''
from threading import stack_size,Thread
sys.setrecursionlimit(10**6)
stack_size(10**8)
'''
def listt():
    return [int(i) for i in input().split()]
 
def gcd(a,b): 
   return math.gcd(a,b) 
 
def lcm(a,b): 
    return (a*b) // gcd(a,b) 

def factors(n):
    step = 2 if n%2 else 1
    return set(reduce(list.__add__,([i, n//i] for i in range(1, int(math.sqrt(n))+1, step) if n % i == 0)))

def comb(n,k):
    factn=math.factorial(n)
    factk=math.factorial(k)
    fact=math.factorial(n-k)
    ans=factn//(factk*fact)
    return ans

def is_prime(n): 
    if n <= 1: 
        return False
    if n == 2: 
        return True
    if n > 2 and n % 2 == 0: 
        return False

    max_div = math.floor(math.sqrt(n)) 
    for i in range(3, 1 + max_div, 2): 
        if n % i == 0: 
            return False
    return True
def maxpower(n,x):
    B_max = int(math.log(n, x)) #tells upto what power of x n is less than it like 1024->5^4
    return B_max
def binaryToDecimal(n): 
    return int(n,2) 
#d=sorted(d.items(),key=lambda a:a[1]) sort dic accc to values
#g=pow(2,6)
#a,b,n,m=map(int,input().split())
#print ("{0:.8f}".format(min(l)))
t=int(input())
for _ in range(t):
    l=listt()
    l.sort()
    if l[0]+l[1]>=l[2]:
        print(math.floor((l[0]+l[1]+l[2])/2))
    else:
        print(l[0]+l[1])    