A12972 | Sweet Problem

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.

The first line contains integer $t$ ( $1 \le t \le 1000$ ) — 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 $b$ ( $1 \le r, g, b \le 10^8$ ) — the number of red, green and blue candies, respectively.

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