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.

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.

Constraints

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

Sample Input 1

5
6 9 6 6 5

Sample Output 1

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.

Sample Input 2

5
0 1 2 1 0

Sample Output 2

No

Sample Input 3

1
10

Sample Output 3

Yes
0 0 10

见题面 Input 部分

见题面 Output 部分