Problem Statement

Given is an $N \times N matrix C$ whose elements are non-negative integers. Determine whether there is a pair of sequences of $non-negative integers A_1,A_2,\ldots,A_N$ and $B_1,B_2,\ldots,B_N$ such that C_{i,j}=A_i+B_j for every (i, j). If the answer is yes, print one such pair.

Input

Input is given from Standard Input in the following format:
N
$C_{1,1} C_{1,2} \ldots C_{1,N}$
$C_{2,1} C_{2,2} \ldots C_{2,N}$
:
$C_{N,1} C_{N,2} \ldots C_{N,N}$

Output

• If no pair A, B satisfies the condition:

Print No in the first line.
No

• If some pair A, B satisfies the condition:

In the first line, print Yes.
In the second line, print the elements of A, with spaces in between.
In the third line, print the elements of B, with spaces in between.
If multiple pairs satisfy the condition, any of them will be accepted.
Yes
$A_1 A_2 \ldots A_N$
$B_1 B_2 \ldots B_N$

Constraints

• $1 \leq N \leq 500$
• $0 \leq C_{i,j} \leq 10^9$

Sample Input 1

3
4 3 5
2 1 3
3 2 4

Sample Output 1

Yes
2 0 1
2 1 3

Note that A and B consist of non-negative integers.

Sample Input 2

3
4 3 5
2 2 3
3 2 4

Sample Output 2

No

见题面 Input 部分

见题面 Output 部分