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.

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15B. Balanced Trio

Constraints

Input

Output

Samples

15B. Balanced Trio

Constraints

Input

Output

Samples