Balanced Trio - Repovive Starter Round 4 | Repovive

15B. Balanced Trio

1000 pts1s256 MB

You are given three integers $a$ , $b$ , and $c$ .

You want to split each of them into two non-negative integer parts:

$a = a_1 + a_2$
$b = b_1 + b_2$
$c = c_1 + c_2$

The split is called balanced if the two triples have equal sums, that is $a_1 + b_1 + c_1 = a_2 + b_2 + c_2$ .

Determine whether a balanced split exists. If it exists, output one valid split.

If several valid answers exist, you may output any of them.

Constraints

$1 \le t \le 10^4$
$0 \le a, b, c \le 1000$

Input

t

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

Output

For each test case, if there is no valid answer, output:

\text{No}

Otherwise, output:

\text{Yes}

a_1 \quad b_1 \quad c_1 \quad a_2 \quad b_2 \quad c_2

If there are multiple valid answers, you may output any of them.

Samples

Input

Case 1

1 2 3

Case 2

0 0 0

Case 3

1 1 1

Explanation

Case 1

For $a=1$ , $b=2$ , and $c=3$ , the shown split gives $1+2+0=3$ and $0+0+3=3$ .

Case 2

All three numbers are zero, so the two sums are both zero.

Case 3

The total amount is $3$ , so it cannot be split into two equal integer sums.

Output

Case 1

Yes
1 2 0 0 0 3

Case 2

Yes
0 0 0 0 0 0

Case 3

No

You are given three integers $a$ , $b$ , and $c$ .

You want to split each of them into two non-negative integer parts:

$a = a_1 + a_2$
$b = b_1 + b_2$
$c = c_1 + c_2$

The split is called balanced if the two triples have equal sums, that is $a_1 + b_1 + c_1 = a_2 + b_2 + c_2$ .

Determine whether a balanced split exists. If it exists, output one valid split.

If several valid answers exist, you may output any of them.

$1 \le t \le 10^4$
$0 \le a, b, c \le 1000$

t

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

For each test case, if there is no valid answer, output:

\text{No}

Otherwise, output:

\text{Yes}

a_1 \quad b_1 \quad c_1 \quad a_2 \quad b_2 \quad c_2

If there are multiple valid answers, you may output any of them.

For $a=1$ , $b=2$ , and $c=3$ , the shown split gives $1+2+0=3$ and $0+0+3=3$ .

The total amount is $3$ , so it cannot be split into two equal integer sums.

My submissions

Announcements

My submissions

Announcements

My submissions

Announcements

My submissions

Announcements

15B. Balanced Trio

Constraints

Input

Output

Samples

15B. Balanced Trio

Constraints

Input

Output

Samples