You are given a grid of size .

Using this grid, you are to generate a new grid of size as follows:

- The first element in each row will be assigned a value of . The array is unknown to you.
- For each element in row , .

A third array, will then be generated as follows:

- The element is the
*median*of the column in .

It is known that the *median* of the array is **exactly** zero. Can you determine any array that makes the median of zero, or state that it is impossible?

**Note**: For odd , the median of the array is the middle element in the sorted array. For even , the median is the *minimum* of the two middle elements in the sorted array. For example, the median of is .

#### Input Specification

The first line will contain the integer .

The next lines will each contain integers, .

#### Output Specification

If it is impossible, print `NO`

on one line.

Otherwise, print `YES`

on the first line.

On the second line, print space separated integers, the array . must fit in a 32-bit integer , or you will receive `Wrong Answer`

.

#### Subtasks

##### Subtask 1 [7%]

##### Subtask 2 [24%]

##### Subtask 3 [69%]

No further constraints.

#### Sample Input For Subtask 1

```
4
2 1 0
3 3 0
1 6 1
1 1 1
```

#### Sample Output For Subtask 1

```
YES
-1 -3 -2 0
```

#### Explanation For Sample For Subtask 1

The array that is generated with the array below is:

```
-1 1 2 2
-3 0 3 3
-2 -1 5 6
0 1 2 3
-----------
-2 0 2 3
```

The median of the array is . Note that there could be multiple answers. For example, is also an answer. You are only required to print *any* one of them.

#### Sample Input For Subtask 2

```
7
1 2 2 2 1 1
3 0 0 1 1 1
0 0 0 0 0 0
1 0 2 1 0 1
2 0 0 1 4 0
2 1 1 2 4 5
1 1 1 1 1 1
```

#### Sample Output For Subtask 2

```
YES
5 1 -2 -3 1 -5 -8
```

#### Sample Input For Subtask 3

```
3
3 -12
-6 3
6 -5
```

#### Sample Output For Subtask 3

```
YES
-1 5 -1
```

## Comments