Sum of Arithmetic Sequences

Jeonghwi is taking a combinatorics course as a math major and is learning the formula for the sum of an arithmetic sequence. The 2023 SCON contest is one week away, but he has not finished even half of the problems. Pretending to go to the restroom, he ran to the Information Science Building and wrote a problem about arithmetic sequences.

Given a sequence $A$ of length $N$, find two arithmetic sequences $B$ and $C$ of length $N$ such that $A_i=B_i+C_i$ holds for every $1\le i\le N$.

A sequence $A=\{ A_1,A_2,\cdots ,A_N \}$ is an arithmetic sequence if $A_i-A_{i-1}$ is the same value for every $i$ with $2\leq i\leq N$. By this definition, any sequence of length $2$ or less is always an arithmetic sequence.

The first line contains the length $N$ of sequence $A$.

The second line contains the elements $A_1,A_2,\cdots ,A_N$ of sequence $A$ in order, separated by spaces.

If there are no two arithmetic sequences $B$ and $C$ of length $N$ that satisfy $A_i=B_i+C_i$ for every $1\leq i\leq N$, print NO on the first line.

Otherwise, print YES on the first line. On the second line, print the elements of $B$, and on the third line, print the elements of $C$, each separated by spaces. If several pairs $B,C$ are possible, print any one of them. If such sequences exist, it can be proven that an output satisfying the constraints exists.

• $1\leq N\leq 10^5$
• $-10^9\leq A_i\leq 10^9$ $(1\le i\le N)$
• $-10^{18}\leq B_i,C_i\leq 10^{18}$ $(1\le i\le N)$
• $A_i$, $B_i$, $C_i$ are all integers $(1\le i\le N)$