#P1492E. Almost Fault-Tolerant Database

    ID: 5809 Type: RemoteJudge 2000ms 512MiB Tried: 0 Accepted: 0 Difficulty: (None) Uploaded By: Tags>brute forceconstructive algorithmsdfs and similargreedyimplementation*2500

Almost Fault-Tolerant Database

No submission language available for this problem.

Description

You are storing an integer array of length mm in a database. To maintain internal integrity and protect data, the database stores nn copies of this array.

Unfortunately, the recent incident may have altered the stored information in every copy in the database.

It's believed, that the incident altered at most two elements in every copy. You need to recover the original array based on the current state of the database.

In case there are multiple ways to restore the array, report any. If there is no array that differs from every copy in no more than two positions, report that as well.

The first line contains integers nn and mm (2n2 \le n; 1m1 \le m; nm250000n \cdot m \le 250\,000) — the number of copies and the size of the array.

Each of the following nn lines describes one of the currently stored copies in the database, it consists of mm integers si,1,si,2,,si,ms_{i, 1}, s_{i, 2}, \dots, s_{i, m} (1si,j1091 \le s_{i, j} \le 10^9).

If there is an array consistent with all given copies, print "Yes" and then the array itself. The array must have length mm and contain integers between 11 and 10910^9 only.

Otherwise, print "No".

If there are multiple possible arrays, print any of them.

Input

The first line contains integers nn and mm (2n2 \le n; 1m1 \le m; nm250000n \cdot m \le 250\,000) — the number of copies and the size of the array.

Each of the following nn lines describes one of the currently stored copies in the database, it consists of mm integers si,1,si,2,,si,ms_{i, 1}, s_{i, 2}, \dots, s_{i, m} (1si,j1091 \le s_{i, j} \le 10^9).

Output

If there is an array consistent with all given copies, print "Yes" and then the array itself. The array must have length mm and contain integers between 11 and 10910^9 only.

Otherwise, print "No".

If there are multiple possible arrays, print any of them.

Samples

Sample Input 1

3 4
1 10 10 100
1 1 1 100
10 100 1 100

Sample Output 1

Yes
1 10 1 100

Sample Input 2

10 7
1 1 1 1 1 1 1
1 1 1 1 1 1 2
1 1 1 1 1 2 2
1 1 1 1 2 2 1
1 1 1 2 2 1 1
1 1 2 2 1 1 1
1 2 2 1 1 1 1
2 2 1 1 1 1 1
2 1 1 1 1 1 1
1 1 1 1 1 1 1

Sample Output 2

Yes
1 1 1 1 1 1 1

Sample Input 3

2 5
2 2 1 1 1
1 1 2 2 2

Sample Output 3

No

Note

In the first example, the array [1,10,1,100][1, 10, 1, 100] differs from first and second copies in just one position, and from the third copy in two positions.

In the second example, array [1,1,1,1,1,1,1][1, 1, 1, 1, 1, 1, 1] is the same as the first copy and differs from all other copies in at most two positions.

In the third example, there is no array differing in at most two positions from every database's copy.