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6A. Maximum Triangle Perimeter

500 ptstype :zen to enter zen mode

Time: 1sMemory: 256 MB

You are given three sticks with integer lengths $a$ , $b$ , and $c$ .

You may cut the sticks. In one cut, you choose one stick and decrease its length by a positive integer. All stick lengths must remain positive integers.

Find the maximum possible perimeter of a non-degenerate triangle that can be made from the three sticks after some cuts. You may also make no cuts.

Constraints

$1 \le t \le 10^4$
$1 \le a, b, c \le 10^9$

Input

t

\left. \begin{array}{l} a \quad b \quad c \end{array} \right\} \times t

Output

\text{ans} \; \} \times t

Samples

Input

Case 1

4 4 4

Case 2

3 4 10

Case 3

1 1 1000000000

Case 4

7 2 4

Case 5

5 6 11

Explanation

Case 1

The sticks are $4,4,4$ . They already make a triangle, and the perimeter is $12$ .

Case 2

We can cut the stick of length $10$ into length $6$ . Then the sticks become $3,4,6$ , and the perimeter is $13$ .

Case 3

We can cut the stick of length $1000000$ into length $1$ . Then the sticks become $1,1,1$ , and the perimeter is $3$ .

Case 4

We can cut the stick of length $7$ into length $5$ . Then the sticks become $5,2,4$ , and the perimeter is $11$ .

Case 5

We can cut the stick of length $11$ into length $10$ . Then the sticks become $5,6,10$ , and the perimeter is $21$ .

Output

Case 1

Case 2

Case 3

Case 4

Case 5

You are given three sticks with integer lengths $a$ , $b$ , and $c$ .

You may cut the sticks. In one cut, you choose one stick and decrease its length by a positive integer. All stick lengths must remain positive integers.

Find the maximum possible perimeter of a non-degenerate triangle that can be made from the three sticks after some cuts. You may also make no cuts.

$1 \le t \le 10^4$
$1 \le a, b, c \le 10^9$

t

\left. \begin{array}{l} a \quad b \quad c \end{array} \right\} \times t

\text{ans} \; \} \times t

The sticks are $4,4,4$ . They already make a triangle, and the perimeter is $12$ .

We can cut the stick of length $10$ into length $6$ . Then the sticks become $3,4,6$ , and the perimeter is $13$ .

We can cut the stick of length $1000000$ into length $1$ . Then the sticks become $1,1,1$ , and the perimeter is $3$ .

We can cut the stick of length $7$ into length $5$ . Then the sticks become $5,2,4$ , and the perimeter is $11$ .

We can cut the stick of length $11$ into length $10$ . Then the sticks become $5,6,10$ , and the perimeter is $21$ .

Maximum Triangle Perimeter - Repovive Premier Round 3 | Repovive | Repovive