Score : $500$ points

Problem Statement

You are given a sequence of $N$ integers $S = (S_1, \ldots, S_N)$. Determine whether there is a sequence of $N+2$ integers $A = (A_1, \ldots, A_{N+2})$ that satisfies the conditions below.

• $0\leq A_i$ for every $i$ ($1\leq i\leq N+2$).
• $S_i = A_{i} + A_{i+1} + A_{i+2}$ for every $i$ ($1\leq i\leq N$).

If it exists, print one such sequence.

Constraints

• $1\leq N\leq 3\times 10^5$
• $0\leq S_i\leq 10^9$

Input

Input is given from Standard Input from the following format:

$N$

$S_1$ $\ldots$ $S_N$

Output

If there is a sequence $A$ that satisfies the conditions, print Yes; otherwise, print No. In the case of Yes, print an additional line containing the elements of such a sequence $A$, separated by spaces.

$A_1$ $\ldots$ $A_{N+2}$

If there are multiple sequences satisfying the conditions, you may print any of them.

5
6 9 6 6 5

Yes
0 4 2 3 1 2 2

We can verify that $S_i = A_i + A_{i+1} + A_{i+2}$ for every $i$ ($1\leq i\leq N$), as follows.

• $6 = 0 + 4 + 2$.
• $9 = 4 + 2 + 3$.
• $6 = 2 + 3 + 1$.
• $6 = 3 + 1 + 2$.
• $5 = 1 + 2 + 2$.

5
0 1 2 1 0

No

1
10

Yes
0 0 10