Score : $400$ points

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.

Constraints

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

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

$A_1$ $A_2$ $\ldots$ $A_N$

$B_1$ $B_2$ $\ldots$ $B_N$

3
4 3 5
2 1 3
3 2 4

Yes
2 0 1
2 1 3

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

3
4 3 5
2 2 3
3 2 4

No